Composition Vendor Newgen KnowledgeWorks (P) Ltd. PLoS One plos plosone PLOS One 1932-6203 Public Library of Science San Francisco, CA USA 10.1371/journal.pone.0328210 PONE-D-24-24548 Research Article Social sciencesSociologyCommunicationsSocial communicationSocial mediaTwitter Computer and information sciencesNetwork analysisSocial networksSocial mediaTwitter Social sciencesSociologySocial networksSocial mediaTwitter Medicine and health sciencesPathology and laboratory medicinePathogenesisHost-pathogen interactions Medicine and health sciencesMedical conditionsInfectious diseasesViral diseasesCOVID 19 Computer and information sciencesNetwork analysisSocial networks Social sciencesSociologySocial networks Social sciencesSociologyCommunicationsSocial communicationSocial media Computer and information sciencesNetwork analysisSocial networksSocial media Social sciencesSociologySocial networksSocial media Research and analysis methodsResearch designSurvey researchSurveys Medicine and health sciencesEpidemiologyPandemics Biology and life sciencesNeuroscienceCognitive scienceCognitive psychologyLanguage Biology and life sciencesPsychologyCognitive psychologyLanguage Social sciencesPsychologyCognitive psychologyLanguage Estimating affective polarization on a social network Affective polarization in social networks https://orcid.org/0000-0002-1625-2435 Hohmann Marilena Conceptualization Data curation Formal analysis Methodology Software Visualization Writing – original draft Writing – review & editing 1 * https://orcid.org/0000-0001-5984-5137 Coscia Michele Conceptualization Methodology Software Writing – original draft Writing – review & editing 2 Copenhagen Center for Social Data Science, University of Copenhagen, Copenhagen, Denmark CS Department, IT University of Copenhagen, Copenhagen, Denmark Gomes Ferreira Carlos Henrique Editor Universidade Federal de Ouro Preto, BRAZIL

The authors have declared that no competing interests exist.

 * E-mail: marilena.hohmann@sodas.ku.dk 2492025 2025 20 9 e0328210 1762024 2562025 2025 Hohmann, Coscia This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Concerns about polarization and hate speech on social media are widespread. Affective polarization, i.e., hostility among partisans, is crucial in this regard as it links political disagreements to hostile language online. However, only a few methods are available to measure how affectively polarized an online debate is, and the existing approaches do not investigate jointly two defining features of affective polarization: hostility and social distance. To address this methodological gap, we propose a network-based measure of affective polarization that combines both aspects – which allows them to be studied independently. We show that our measure accurately captures the relation between the level of disagreement and the hostility expressed towards others (affective component) and whom individuals choose to interact with or avoid (social distance component). Applying our measure to a large-scale Twitter data set on COVID-19, we find that affective polarization was low in February 2020 and increased to high levels as more users joined the Twitter discussion in the following months.

 The author(s) received no specific funding for this work. Data Availability Data cannot be shared publicly as restrictions of the European Union’s General Data Protection Regulation (GDPR) apply. All information needed to re-collect the data is provided in the Materials & Methods section. The code needed to reproduce the results of the synthetic experiments is provided in the paper. Introduction

Affective polarization describes the affective attitude towards like-minded and disagreeing others. Traditionally, surveys are used to measure affective polarization [1]. Survey respondents are, for instance, asked to indicate how they feel toward others with opposing political views or whether they would want an out-group member to be their colleague or friend. When participants feel more hostile towards the out-group than the in-group, affective polarization is high.

Social identity and group dynamics are central to affective polarization, but collecting information on social ties in surveys is challenging. Since this information is usually unavailable in survey data, a relevant conceptual component of affective polarization often remains undiscovered in these standard survey measures. Moreover, while surveys can provide detailed information on attitudes and intentions, this data might not necessarily reflect actual behavior [2]. Although a respondent might claim to dislike or avoid others they disagree with, a survey cannot conclusively clarify whether the participant indeed acts upon these intentions in everyday life [1,3].

Complementary to surveys, social media has emerged as a relevant domain for studying affective polarization [4–6]. On social media, large-scale group dynamics can be directly observed by considering the social network structures through which users interact. This raises the question: How can we measure affective polarization in a social network?

The most common approach to estimating affective polarization examines the average feelings or sentiment toward the in-group versus out-group [4,6–10]. This measure requires survey respondents or social media users to be divided into two groups. The resulting quantification of affective polarization is relatively crude because people are split into two groups regardless of nuances in political attitudes, such as being moderately conservative or extremely liberal.

A second type of approach involves correlational methods to quantify, for instance, the relation between the strength of policy preferences and how individuals feel toward others with different political ideas [11]. An advantage of this approach is that it is more nuanced than splitting the respondents into two categories. However, neither of the approaches discussed so far can account for how social interactions are organized, which is a crucial indicator of affective polarization.

Some network-based methods explicitly modeling those social relations exist, such as a measure proposed in [5]. The authors split Twitter users into two groups and then measure the sentiment of the interactions within and between groups. While this method considers the social network, it still requires users to be split into two camps. As argued above, such a measure cannot account for fine-grained distinctions between political leanings.

Another group of network-based methods analyzes signed graphs [12–14]. In a signed network, each edge has a positive or negative sign, depending on the type of interaction between two individuals. Measures on signed graphs can capture how the positive or negative interactions align with the network structure. However, they cannot account for nuances in how people interact, such as mild vs. extreme hostility, since the edge signs are too coarse to capture this information.

In summary, current measures of affective polarization face three main challenges: they are insensitive to information on individuals’ opinions, the valence of their interactions, or the structure of these interactions. In this paper, we propose a measure that overcomes these issues. Firstly, our method explicitly considers the structure of interactions in a social network. This allows us to quantify social distance, i.e., whether individuals avoid others they disagree with. Secondly, the proposed measure captures the relationship between political opinions and animosity. Our framework models both opinions and hostility as continuous variables. Consequently, we do not need to divide individuals into two groups or compress information regarding the hostility between people into binary edge signs.

In experiments on synthetic data, we show how our measure summarizes the relation between disagreement and hostility (affective component) and information on social interactions (social distance component) in a single affective polarization score. Since the components are distinct, the method allows for the estimation of affective polarization even without considering the social distance component, as in some frameworks the social distance component is regarded as a different dimension, rather than a component, of affective polarization [15].

Moreover, we compare our score to the alternative methods we review above. Subsequently, we apply this measure to a data set of approximately 47 million tweets discussing the COVID-19 pandemic, which US-based users posted to Twitter between February 2020 and July 2020. We find that the Twitter debate was not affectively polarized in February 2020 but became increasingly polarized as more users joined the discussion in the subsequent months.

 Affective polarization measure

The survey-based literature has developed various questionnaire items to measure affective polarization, which can be grouped into two categories: items focusing on hostility and items focusing on social distance. Following this literature, we define two components of affective polarization:

Affective component: Since affective polarization describes increasing dislike or distrust between political opponents, affect is a central element to consider [1,2,9,11,16–20]. While affective polarization can refer to either in-group favoritism or out-group hostility, empirical studies have often prioritized out-group hostility [1,16,21]. Therefore, we focus on hostility here and, in particular, on the relationship between disagreement and hostility. If there is no relation, each individual treats all others in an equally (non-)hostile way, regardless of their opinions, and affective polarization is therefore low (Fig 1a, example on the left). However, if people are increasingly hostile the more they disagree, then affective polarization is high (Fig 1a, example on the right).

Social distance component: Prior survey research has used social distance as an indicator of affective polarization [2,9,11,22]. Social distance survey items assess people’s willingness to form social ties across political divides, such as having an out-group member as a friend, neighbor, or in-law [2]. These studies demonstrate that affective polarization shapes social interactions by influencing whom individuals choose to engage with or avoid.

This aspect of affective polarization can be observed by analyzing the structure of interactions between individuals in a social network: If people interact regardless of their political opinion, social distance is small (Fig 1b, example on the left). In contrast, if people interact with like-minded individuals but avoid communities holding opposing views, social distance is large. In social media research, this aspect is also referred to as interactional polarization [6,7].

 10.1371/journal.pone.0328210.g001Components of affective polarization.

(a) Affective component: no relation between disagreement and hostility on the left, strong correlation between disagreement and hostility on the right. (b) Social distance component: individuals are randomly connected in the left graph, whereas there are distinguishable, politically aligned communities in the right graph.

 Definition

Since both affect and social distance describe the same underlying concept of affective polarization, we argue that a comprehensive measure should capture both components in a single score. We define such a measure in the following section.

 Formulation

We consider a connected, undirected, and unweighted network G=(V,E) with V as the set of individuals and E⊆V×V as the set of connections. We record an opinion value oi∈[−1,1] per node in V. For each edge between two nodes i and j, we determine a disagreement value xi,j as the absolute opinion difference xi,j=|oi−oj| for each pair of nodes directly connected by an edge. Moreover, we document a hostility value yi,j∈[0,1] per edge. An edge represents an interaction between two individuals, such as a reply or an @-mention on a social media platform or a friendship tie in an offline context. We assume that the edges in E are undirected because we want to examine how often and how hostile the interactions between individuals with different political views are. In this macro-level view, it is irrelevant whether liberals address conservatives in a hostile manner or vice versa.

We represent the oi, xi,j, and yi,j values as vectors. Given the network G, opinions o, and hostility y, our measure αo,y,G quantifies the relation between disagreement and hostility (affective component) while considering the structure of social interactions (social distance component). To outline how αo,y,G is defined, we first discuss how the two components can be measured separately.

Affective component. To quantify the affective component, we use the Spearman rank correlation coefficient ρ~o,y, which measures the monotonic relationship between two variables. It is well-suited to capture the association between the disagreement vector x and the hostility vector y, regardless of whether this relationship is linear. As our Twitter analysis shows, real-world data may be skewed and exhibit nonlinear relationships (see Sect 3 of the S1 File). We therefore opt for the Spearman rank correlation coefficient in the definition of our measure.

Various scenarios are possible: If ρ~o,y>0, increasing disagreement coincides with increasing hostility. In other words, there is polarization in the affective component. If ρ~o,y=0, disagreement and hostility are unrelated, and there is no affective polarization. If ρ~o,y<0, we do not observe affective polarization. In this case, disagreement and hostility are negatively related; i.e., the more people agree, the more hostile they are toward each other. Although it is rather unlikely that this will occur empirically, it is relevant for our measure to distinguish this scenario from the others. The Spearman rank correlation coefficient is defined as follows:

ρ~o,y=1−6∑di,j2n(n2−1)

where di,j is the difference in rank between the disagreement values xi,j=|oi−oj| and the hostility values yi,j for each connected node pair in G, and n is the number of such pairs.

As argued above, we use the Spearman correlation because real-world data may be skewed. However, the Pearson correlation ρo,y could also be used if the data exhibits a linear relationship. A definition of the Pearson correlation coefficient is provided in Sect 1 of the S1 File.

Social distance component. The social distance component describes the structure of interactions between people with similar vs. opposing political opinions. We rely on the recently introduced Generalized Euclidean (GE) polarization measure δG,o [23] to quantify this component. By combining opinion data with network information, δG,o can quantify 1) the distribution of opinions, 2) the level of structural separation in the network, and 3) how the opinions are aligned with the network structure. The measure is defined as [23]:

δG,o=(o+−o−)TL†(o+−o−)

where o +  is a vector containing all positive opinions and zero otherwise, o−- is a vector containing the absolute value of all negative opinions and zero otherwise, and L† is the pseudoinverse of the Laplacian matrix of the network G.

Affective polarization measure αo,y,G. By combining the Pearson correlation and the Generalized Euclidean distance, we can obtain an affective polarization score that includes both the affective and the social distance component:

αo,y,G=ρ~o,yδG,o.

We multiply the two components to preserve the sign flip from a negative to a positive correlation in ρ~o,y. The sign of our measure αo,y,G can therefore be interpreted similarly to the sign of the Spearman rank correlation: if αo,y,G>0, there is affective polarization; if αo,y,G=0, there is no affective polarization; and if αo,y,G<0, there is a third scenario in which low disagreement co-occurs with high hostility.

In general, αo,y,G takes values from an arbitrary negative to an arbitrary positive number. The higher the αo,y,G value, the higher the level of affective polarization.

 Results

We conduct experiments with synthetic data to demonstrate how our measure captures both the affective component and the social distance component and to compare it to other methods currently used in the literature. Subsequently, we apply our measure to a series of real-world Twitter networks in which users discuss COVID-19 restrictions.

Method validation

We compare our measure αo,y,G to other affective polarization methods proposed in the literature:

μo,y: The average sentiment score μo,y enables a comparison between the mean in-group vs. mean out-group hostility [4,6–10]. We report two values: Avg μo,y (Like-minded) which summarizes the average hostility for all like-minded node pairs, and Avg μo,y (Cross-cutting) which summarizes the average hostility among all disagreeing node pairs.

ρo,y: The Pearson correlation coefficient ρo,y measures the linear relationship between the disagreement vector x and hostility vector y.

EMDo,y,G: This measure, which combines the Earth Mover’s Distance and Krackhardt’s E/I index, focuses on network-based interactions [5]. It splits users into two groups and measures sentiment within and between these groups. For each group, we calculate one score that captures the difference between in-group versus out-group hostility.

SAIo,y,G: The Structural Alignment Index SAIo,y,G examines the alignment between edge signs and network structure by measuring frustration in a signed network [12].

POLEy,G: This method calculates the node-level Pearson correlation between transition probabilities on a signed and unsigned network. The final polarization measure, POLEy,G, is the average of these node-level scores [13].

Sect 1 in the S1 File contains further details of how these measures are defined. Some of the alternative measures, μo,y, EMDo,y,G, and SAIo,y,G, require the nodes to be split into two groups. These groups could, for instance, represent climate change believers and disbelievers [5] or Democrats and Republicans. In the experiments below, we split the nodes into a blue and a red group. All values shown in the following figures represent the lower and upper bound of a 95% confidence interval, which we calculate across 100 experiment repetitions.

The affective component.

The affective component describes the relationship between disagreement and hostility. Since this relation is characterized by the joint distribution of disagreement values x and hostility values y, a comprehensive measure should quantify both aspects. Therefore, we split the affective component experiments into two subsections. First, we test the measures’ sensitivity to changes in the hostility distribution, followed by changes in the disagreement distribution.

 Hostility Distribution.

Fig 2 summarizes the experiment on changes in the hostility distribution. We generate a random graph and assign opinion values from –1 to  + 1 to the nodes. The network structure and the opinion values stay fixed for all experiments (a) to (e). As shown in the scatter plots in Fig 2, we only change the hostility value assigned to each edge between two nodes.

10.1371/journal.pone.0328210.g002Affective component (hostility distribution).

From top to bottom: network where the node color reflects opinion, from –1 (blue), passing 0 (white), to  + 1 (red); scatter plot with disagreement on the x-axis and hostility on the y-axis; values of αo,y,G, ρo,y, μo,y, EMDo,y,G, SAIo,y,G, and POLEy,G. The results (in parentheses) denote the lower and upper bound of the 95% confidence interval across 100 repetitions of the experiment.

In (a) and (b), hostility decreases as disagreement increases. This relation gets weaker from (a) to (b); and in (c), the two variables are entirely uncorrelated. In (d) and (e), hostility and disagreement are positively related, and we expect the highest level of affective polarization in these cases.

The affective polarization measure αo,y,G, the Pearson correlation ρo,y, and EMDo,y,G confirm this expectation as they increase from (a) to (e). We conclude that these measures can account for changes in the hostility distribution.

Similarly, the average sentiment score μo,y can, for the most part, account for changes in the hostility distribution. As expected, the average hostility among like-minded individuals Avg μo,y (Like-minded) decreases from (a) to (e). However, Avg μo,y (Cross-cutting) cannot consistently capture the increasing hostility among disagreeing individuals as the confidence intervals overlap.

Lastly, the measures working with signed networks, SAIo,y,G and POLEy,G cannot fully capture changes in the hostility distribution. While SAIo,y,G accounts for the sign flip going from a negative disagreement–hostility relation to a positive one, the measure is not sensitive to the strength of the correlation. The values in (a) and (b) are the same, and so are the values in (d) and (e). The same shortcoming applies to POLEy,G. Moreover, POLEy,G cannot capture the sign of the correlation changing, and it returns the highest values in example (c), where disagreement and hostility are entirely uncorrelated.

 Disagreement distribution.

We now turn to the second aspect of the affective component: the distribution of disagreement values. As before, we generate a random graph and assign opinion values between –1 and  + 1 to the nodes. We update the opinions of a few nodes so that the overall level of disagreement increases slightly from (a) to (e). Then, we assign hostility values to the edges. Importantly, we use the same hostility vector y across all the examples in Fig 3. Since the disagreement values x change, while the hostility values y stay fixed, the correlation between x and y gets stronger, as shown in the scatter plots in Fig 3.

10.1371/journal.pone.0328210.g003Affective component (disagreement distribution).

Same legend as Fig 2.

We find that both the affective polarization measure αo,y,G and the Pearson correlation ρo,y are sensitive to changes in the disagreement distribution. Conversely, μo,y, EMDo,y,G, SAIo,y,G, and POLEy,G cannot distinguish between any of the examples (a) to (e). These measures split the nodes into groups and, therefore, cannot capture changes in the in-group disagreement distribution. Importantly, these differences cause the disagreement–hostility relation, and thus the level of affective polarization, to increase from (a) to (e). In short, μo,y, EMDo,y,G, SAIo,y,G, and POLEy,G are insensitive to this aspect of the affective component.

 The social distance component.

The third experiment focuses on the social distance component. We generate a network with a community of blue nodes and a community of red nodes. The opinion, disagreement, and hostility values are fixed across the examples (a) to (e). Consequently, the disagreement–hostility relation is the same for all networks, as shown in the scatter plots in Fig 4. However, the network structure changes from (a) to (e). As the connections between the two communities become sparser, social distance increases, and we therefore expect the affective polarization level to increase from (a) to (e).

10.1371/journal.pone.0328210.g004Social distance component.

Same legend as Fig 2.

Fig 4 confirms that our affective polarization measure αo,y,G is sensitive to the social distance component: αo,y,G increases from (a) to (e) as expected. POLEy,G can only partly capture this component. While the POLEy,G values increase from (a) to (e), some of the confidence intervals overlap.

μo,y (Cross-cutting), EMDo,y,G and SAIo,y,G decrease from (a) to (e), suggesting that network (e) is the least polarized example. This result is not in line with expectations, and these measures consequently do not appropriately capture changes in the social distance component. Lastly, the Pearson correlation coefficient ρo,y cannot account for changes in this component as the results are the same across all networks.

 Summary.

Table 1 summarizes the results. From the experiments, we conclude that our proposed measure αo,y,G is the only method tested here that can appropriately capture changes in the hostility and disagreement distributions (affective component) and changes in the structure of social interactions (social distance component). In Sect 2 of the S1 File, we also confirm that αo,y,G can capture changes related to the nodes’ opinion strength. In this additional experiment, we show that αo,y,G is the only method that can detect an increase in affective polarization due to uniformly more extreme opinions.

10.1371/journal.pone.0328210.t001Summary of the synthetic experiments.
Affective component Social distance component
Hostility Disagreement
αo,y,G ✓ ✓ ✓
ρo,y ✓ ✓ ✗
μo,y (✓) ✗ ✗
EMDo,y,G ✓ ✗ ✗
SAIo,y,G (✓) ✗ ✗
POLEy,G ✗ ✗ (✓)

Importantly, our affective polarization measure αo,y,G can summarize the affective and the social distance component in a single affective polarization score. This enables comparisons across several networks, for instance, of people discussing different political issues. For longitudinal analyses, like the Twitter analysis we perform below, it is useful to obtain a single score for each network to track changes over time.

Simultaneously, we can decompose this score to study the two components independently. The Spearman rank correlation coefficient ρ~o,y quantifies the affective component, while the Generalized Euclidean distance δG,o measures the social distance component. As we show in the following section, analyzing ρ~o,y and δG,o separately provides further insights into the drivers of affective polarization.

 Twitter data

In addition to the synthetic data presented above, we apply our measure αo,y,G to real-world social media data. Specifically, we analyze a large-scale data set of tweets discussing COVID-19 restrictions between February and July 2020. This allows us to trace the development of affective polarization in the COVID-19 debate on Twitter during the first half year of the pandemic.

By assessing the retweet behavior observed in a sample of 47 million pandemic-related tweets, we infer the ideological leaning of 95,000 Twitter users (see Materials and Methods for details). We use a toxic language classifier to determine how friendly or hostile these users are toward others. Focusing only on tweets containing @-mentions or direct replies, we retrieve a user interaction network for each week between February and July 2020. We analyze both the overall level of affective polarization during this time as well as the affective and social distance component separately.

In early February 2020, we find very low affective polarization in the Twitter data, as indicated by αo,y,G values close to 0 (Fig 5A, week 6). This absence of polarization is expected given that COVID-19 had not been declared a global pandemic and was not the primary topic of public debate yet. Consequently, the engagement on Twitter was limited, involving only a few hundred users in the discussion networks in February 2020.

10.1371/journal.pone.0328210.g005COVID-19 debate on Twitter.

For each week between February and July 2020, the figure shows: (A) the overall level of affective polarization (αo,y,G), (B) the affective component (ρ~o,y), and (C) the social distance component (δG,o). (B) and (C) provide a decomposition of the overall affective polarization score shown in (A).

In week 8, ρ~o,y sharply increases, signaling a rise in polarization driven by the affective component. This is followed by an increase in the social distance component, δG,o, the next week. Interestingly, the two components evolve differently: while ρ~o,y (hostility among disagreeing users) decreases again after an initial spike, δG,o (social distance) remains high during the spring and summer months. This suggests that, initially, there is intense hostility among users who disagree. Over time, these users start avoiding each other, preferentially engaging with those who share the same opinion. As a result, hostility decreases due to fewer interactions between disagreeing users. This underscores the importance of considering both affect and social distance when analyzing affective polarization dynamics.

For the overall level of affective polarization, we find that αo,y,G reaches a first peak in mid-March when the World Health Organization declared COVID-19 a global pandemic. As a response, the United States government introduced a travel ban, and different US states started issuing stay-at-home orders and implementing statewide shutdowns.

We see a second peak in early April when the Centers for Disease Control and Prevention started recommending face masks as a preventive measure, although officials had discouraged wearing face masks until that point [24]. We analyze user references to restrictions-related terms to examine whether this was reflected in Twitter discussions. Notably, the terms mask and test dominated the Twitter discussion in weeks 15–17, indicating that Twitter users picked up on the face mask policy change in their discussions during April 2020.

Fig 5 shows the highest αo,y,G values in July 2020. The keyword analysis indicates that, apart from the terms test and mask, the keyword school is among the three most frequently used terms in the sample at this point. This coincides with an intense public debate about whether or not to reopen schools after the summer break [25], and the results presented here indicate that Twitter users engaged in this heated debate online.

 Discussion

In this paper, we set out to assess affective polarization in a social network across two dimensions: one concerning whether individuals respond to disagreement with hostility (affective component) and the other quantifying the structure of social interactions (social distance component).

We introduce a method that computes the correlation between a disagreement and a hostility vector while considering the structure of the social network. Our measure is sensitive to both components of affective polarization and summarizes them in a single score. As the Twitter data analysis shows, having one unified score proves especially useful for cross-network comparisons and the temporal analysis of affective polarization.

While the ease of comparability is an advantage of this approach, it is important to highlight that the score can also be decomposed into its two components. This facilitates a more in-depth analysis of the factors that drive affective polarization dynamics, as we show in the Twitter analysis. It also allows the use of our method in alternative polarization frameworks, where – differently from here – the social distance component is regarded as a different dimension, rather than a component, of affective polarization.

The work presented here has several limitations that can be addressed in future studies. First, our method relies on a one-dimensional ideological scaling, i.e., it can only consider opinion scores between –1 and  + 1. When applied to countries other than the United States, we would need a different ideological scale that accounts for a multi-party system. Second, our affective dimension solely focuses on hostility. We do so following the definition predominantly used in the literature. Future work could explore in-group friendliness rather than out-group hostility or analyze other social connections, such as trust, respect, or support.

In addition to introducing an affective polarization measure, we also apply our method to a large-scale Twitter data set in order to analyze the development of online affective polarization during the first half of 2020. The results demonstrate a substantial rise in affective polarization, shifting from low levels in February 2020 to high levels during the spring and summer. These findings align with previous research. We expect elevated levels of polarization in political debates, even on previously unknown topics like COVID-19, given the consistent upward trend in affective polarization in the United States since the 1960s [26]. Our analysis confirms this: as soon as COVID-19 gained public and political attention, along with a critical mass of users engaging in the conversation, affective polarization surged on Twitter.

Further research is needed to clarify in which contexts affective polarization is especially high on social media. This question could, for instance, be tackled by analyzing social media samples collected during election versus non-election times. Since elections are moments of intense partisan conflict, these events will likely be accompanied by increased levels of affective polarization [27,28].

The Twitter data analysis we present is subject to several limitations, especially concerning the sampling strategy. Our data collection relies on a compilation of COVID-19-related tweets from prior research [29]. The initial set of keywords used for sampling did not include terms that reflect criticism, ridicule, or skepticism towards the pandemic. Consequently, the data set primarily comprises liberal-leaning users, while the representation of pandemic-skeptic users is relatively limited (see Sect 3 in the S1 File). While this strong liberal leaning is consistent with other analyses on the ideological divide in the US-based pandemic debate on Twitter [30], the results should nevertheless be interpreted cautiously, given that the sampling might not be representative. Moreover, it is important to note that we only consider a small fraction of users and tweets in the final analysis due to the different preprocessing and filtering steps (see Sect 3 in the S1 File). This problem is common to many studies of polarization on social media, and further insight is needed on how representative the results are for the entirety of social media users.

 Materials and methods Data and code availability

The code needed to replicate the results of the synthetic experiments can be found at https://github.com/marilenahohmann/affective-polarization-measure.

The Twitter data collection and analysis complied with the terms and conditions of the Twitter API at the time of retrieval (spring 2022). Since this data set contains personally identifiable data relating to natural persons and the processing took place within the European Union, it is subject to the General Data Protection Regulation (GDPR). Due to these regulations, we cannot make the Twitter data publicly available.

 Synthetic data generation

This section summarizes how G, o, and y are generated in the different experiments:

Network G. We use two different approaches to create the networks: In Figs 2 and 3, we generate a random Gn,m graph with n = 50 nodes and m = 610 edges. The network structure remains the same throughout all examples shown in these figures.

In Fig 4, we generate two cliques of 25 nodes connected by one edge. This network has the same density as the random graphs in Figs 2 and 3. Then, we rewire the network by replacing an edge within one of the cliques by an edge between the cliques. While rewiring the network, we keep the disagreement value of the old and new edge the same (± a margin of 0.05). The number of rewired edges is specified by the parameter r: (a) r = 150; (b) r = 50; (c) r = 10; (d) r = 1; (e) r = 0.

Opinion vector o. In Figs 2 and 4, we generate 25 equispaced opinion values oi∈[0.01,1]. The opinion values are summarized in a vector o* which we use to construct the final vector o=(o*,−o*).

In Fig 3, we again start by generating an opinion vector o* comprising 25 equispaced opinion values oi∈[0.01,1]. We modify this vector by replacing the first 3 opinions with a specified value: (a) o1=o2=o3=0.01; (b) o1=o2=o3=0.125; (c) o1=o2=o3=0.25; (d) ao1=o2=o3=0.5; (e) o1=o2=o3=1.0. Then, the final opinion vector is (o ,–o ).

Disagreement vector x. Across all experiments, we obtain the disagreement vector x by calculating the absolute opinion difference xi,j=|oi−oj| for each pair of nodes directly connected by an edge in G. The disagreement values are between 0 (no disagreement) and 2 (maximum disagreement).

Hostility vector y. The hostility vector y is derived from the disagreement vector x. Each entry yi,j is drawn from a random uniform distribution with bounds xi,j/2±a, where a determines the strength of the correlation. If a = 0, then yi,j=xi,j/2, resulting in a perfect linear correlation. If a = 1, then yi,j can be any value between 0 and 1, leading y to be uncorrelated with x. We can generate negative correlations by taking 1−(xi,j/2±a) instead. In Figs 3 and 4, we generate a positive correlation with a = 0.25.

In Fig 2, we use the old hostility value yi,j and a parameter b to modify the distribution. We re-draw each new hostility value yi,j′ from a random uniform distribution with bounds yi,j±b. Importantly, we impose two constraints on these intervals: If yi,j≤0.5, the interval is limited by 0 as the lower and 0.5 as the upper bound; if yi,j>0.5, it is limited by 0.5 as the lower and 1.0 as the upper bound. In other words, we ensure that any initial hostility values yi,j≤0.5 remain within [0,0.5], and any values yi,j>0.5 remain within (0.5,1.0]. We introduce these constraints to highlight a shortcoming of EMDo,y,G, SAIo,y,G and POLEy,G: These measures categorize all non-hostile interactions (yi,j≤0.5) and all hostile interactions (yi,j>0.5) into two distinct groups without considering the actual distribution of hostility values within these groups.

In Fig 2, we specify the following parameters: (a) negative correlation with a = 0.01 (we do not modify the initial hostility vector and b, therefore, remains unspecified); (b) negative correlation with a = 0.01 and b = 0.25; (c) no correlation: a = 1.0, b is unspecified; (d) positive correlation with a = 0.01, b = 0.25; (e) positive correlation with a = 0.01, b is unspecified.

 Twitter data collection

Our data collection draws on a large, longitudinal COVID-19 tweet data set [29], previously used in other studies of COVID-19 online discussions [31–36]. This data set contains geo-location information that the authors inferred from the tweet and meta-data available for each tweet. There are five types of location tags available: (1) geo-coordinates which are available for users who enabled GPS tracking in their privacy settings; (2) place-bounding boxes which contain a GPS location tag within a specific tweet; (3) profile descriptions where users can specify a location in a free-text field; (4) user locations which public profiles, such as companies, can use to indicate where they are based; and (5) places mentioned in the tweet text. Using the geo-locations inferred through (1)–(4) and the tweet IDs provided in this data set, we collect the content, user information, and metadata for tweets by users in the United States between February and July 2020. We focus on US-based users since national borders confined COVID-19 policies, and the online debates surrounding restrictions, therefore, were highly country-specific.

Importantly, our Twitter data set differs from the original one presented in [29] since some users may have deleted or deactivated their accounts. Additionally, the Twitter API only returned publicly accessible tweets, thus excluding messages from users who changed their account privacy settings.

As part of the data preprocessing, we identify all English-language tweets using a pre-trained language detection model [37], and we filter the data set so that the remaining tweets contain at least one keyword related to COVID-19 restrictions. The initial keywords in this list are manually curated and supplemented by semantically similar words, which we found by training a word2vec model [38]. The final data set contains approximately 47 million tweets by 4.1 million users. Sect 3 of the S1 File provides details on the preprocessing and filtering steps.

We rely on users’ retweet patterns to determine their political leanings. We compile a list of Twitter accounts for the 118th US Congress members (2019-2021) and assign a score from –1 (liberal) to  + 1 (conservative) to each account using the politician’s DW-NOMINATE scores [39,40]. Additionally, we curate a list of media accounts and we use the political leaning scores provided on mediabiasfactcheck.com to assign a score between –1 and  + 1 to each news media account. Lastly, we calculate each user’s opinion score oi as the weighted average of the political and media accounts the user retweeted. In the subsequent analysis, we only consider users who retweeted at least five posts to ensure that the opinion scores reflect an actual preference for liberal or conservative content and are not just the result of retweeting viral posts.

Next, we quantify whether users address each other in a hostile manner. While previous studies have often relied on sentiment [4–6,10], we choose toxic language instead [7]. The overall sentiment in the COVID-19 debate was very negative because of the topics users discuss, such as death, disease, or isolation, which should not be confused with out-group hostility. We, therefore, use a toxicity classifier to determine whether users resort to toxic language when addressing others they disagree with [37].

Lastly, we partition the data set into subsets, each covering a week from Monday to Sunday to mitigate any potential weekday or weekend effects. Within these subsets, we collect all direct interactions – replies and @-mentions – between two individuals, provided we have their respective opinion scores. We use the opinion scores to calculate a disagreement value xi,j for each direct edge between two users. Since there can be more than one reply or @-mention between two users, we calculate the average toxicity of all their interactions and use those as the hostility values yi,j. We extract the largest connected component from each undirected interaction network formed by replies and @-mentions. We use the largest connected component and the o, x, and y vectors to calculate the affective polarization score αo,y,G for each week in the data set.

 Supporting information Supplementary materials.

Document including supporting analyses, figures, tables, and references.

(PDF)

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Political polarization on the digital sphere: a cross-platform, over-time analysis of interactional, positional, and affective polarization on social media. Political Communication. 2021;38(1–2):98–139. Falkenberg M, Zollo F, Quattrociocchi W, Pfeffer J, Baronchelli A. Affective and interactional polarization align across countries. 2023. https://arxiv.org/abs/2311.18535 Lerman K, Feldman D, He Z, Rao A. Affective polarization and dynamics of information spread in online networks. NPJ Complexity. 2024;1(1). Iyengar S, Sood G, Lelkes Y. Affect, not ideology. Public Opinion Quarterly. 2012;76(3):405–31. Mentzer K, Fallon K, Prichard J, Yates DJ. Measuring, unpacking affective polarization on Twitter: the role of party and gender in the 2018 Senate races. In: Proceedings of the 53rd Hawaii International Conference on System Sciences. 2020. Webster SW, Abramowitz AI. The ideological foundations of affective polarization in the U.S. electorate. American Politics Research. 2017;45(4):621–47. Fraxanet E, Pellert M, Schweighofer S, Gómez V, Garcia D. Unpacking polarization: antagonism and alignment in signed networks of online interaction. PNAS Nexus. 2024;3(12):pgae276. doi: 10.1093/pnasnexus/pgae276 39703230 Huang Z, Silva A, Singh A. POLE: polarized embedding for signed networks. In: Proceedings of the Fifteenth ACM International Conference on Web Search and Data Mining. 2022. p. 390–400. Talaga S, Stella M, Swanson TJ, Teixeira AS. Polarization and multiscale structural balance in signed networks. Commun Phys. 2023;6(1):349.doi: 10.1038/s42005-023-01467-8 Schedler A. Rethinking political polarization. Political Science Quarterly. 2023;138(3):335–59. Druckman JN, Klar S, Krupnikov Y, Levendusky M, Ryan JB. Affective polarization, local contexts and public opinion in America. Nat Hum Behav. 2021;5(1):28–38. doi: 10.1038/s41562-020-01012-5 33230283 Dias N, Lelkes Y. The nature of affective polarization: disentangling policy disagreement from partisan identity. American J Political Sci. 2021;66(3):775–90. doi: 10.1111/ajps.12628 Rogowski JC, Sutherland JL. How ideology fuels affective polarization. Political Behavior. 2016;38(2):485–508. Klar S, Krupnikov Y, Ryan JB. Affective polarization or partisan disdain?. Public Opinion Quarterly. 2018;82(2):379–90. Mason L. A cross-cutting calm: how social sorting drives affective polarization. Public Opinion Quarterly. 2016;80(S1):351–77. Bougher LD. The correlates of discord: identity, issue alignment, and political hostility in polarized America. Polit Behav. 2016;39(3):731–62. doi: 10.1007/s11109-016-9377-1 Knudsen E. Affective polarization in multiparty systems? Comparing affective polarization towards voters and parties in Norway and the United States. Scandinavian Political Studies. 2021;44(1):34–44. Hohmann M, Devriendt K, Coscia M. Quantifying ideological polarization on a network using generalized Euclidean distance. Sci Adv. 2023;9(9):eabq2044. doi: 10.1126/sciadv.abq2044 36857460 Centers for Disease Control and Prevention. CDC museum COVID-19 timeline; 2022. https://www.cdc.gov/museum/timeline/covid19.html. Grossmann M, Reckhow S, Strunk KO, Turner M. All states close but red districts reopen: the politics of in-person schooling during the COVID-19 pandemic. Educational Researcher. 2021;50(9):637–48. Garzia D, Ferreira da Silva F, Maye S. Affective polarization in comparative and longitudinal perspective. Public Opin Q. 2023;87(1):219–31. doi: 10.1093/poq/nfad004 37113999 Hansen KM, Kosiara-Pedersen K. How campaigns polarize the electorate: political polarization as an effect of the minimal effect theory within a multi-party system. Party Politics. 2017;23(3):181–92. Hernández E, Anduiza E, Rico G. Affective polarization and the salience of elections. Electoral Studies. 2021;69. Imran M, Qazi U, Ofli F. TBCOV: two billion multilingual COVID-19 tweets with sentiment, entity, geo, and gender labels. Data. 2022;7(1). Lazer D, Ruck DJ, Quintana A, Shugars S, Joseph K, Grinberg N, et al. Report #18: Covid-19 fake news on Twitter. 2020. https://www.covidstates.org/reports/covid-19-fake-news-on-twitter Wang S, Huang X, Hu T, She B, Zhang M, Wang R, et al. A global portrait of expressed mental health signals towards COVID-19 in social media space. Int J Appl Earth Obs Geoinf. 2023;116:103160. doi: 10.1016/j.jag.2022.103160 36570490 Chen Q, Wang W, Huang K, Coenen F. Zero-shot text classification via knowledge graph embedding for social media data. IEEE Internet of Things Journal. 2022;9(12):9205–13. Jia S, Chen Q, Wang W. Covid-19 tweets analysis with topic modeling. In: 2021 4th International Conference on Computing and Big Data. 2021. p. 68–74. Trad R, Spiliopoulou M. Juxtaposing 5G coronavirus tweets with general coronavirus tweets during the early months of coronavirus outbreak. In: 2021 IEEE 34th International Symposium on Computer-Based Medical Systems (CBMS). 2021. p. 597–602. Zhunis A, Lima G, Song H, Han J, Cha M. Emotion bubbles: emotional composition of online discourse before and after the COVID-19 outbreak. In: Proceedings of the ACM Web Conference 2022 . 2022. p. 2603–13. Goetz SJ, Heaton C, Imran M, Pan Y, Tian Z, Schmidt C, et al. Food insufficiency and Twitter emotions during a pandemic. Appl Econ Perspect Policy. 2022:10.1002/aepp.13258. doi: 10.1002/aepp.13258 35572046 Hanu L, Unitary Team. Detoxify. 2020. https://github.com/unitaryai/detoxify Mikolov T, Chen K, Corrado G, Dean J. Efficient estimation of word representations in vector space. 2013. https://arxiv.org/abs/1301.3781 Poole KT, Rosenthal HL. Congress: a political-economic history of roll call voting. Oxford University Press; 1997. Lewis JB, Poole K, Rosenthal H, Boche A, Rudkin A, Sonnet L. Voteview: congressional roll-call votes database. 2022. https://voteview.com/ 10.1371/journal.pone.0328210.r001 Decision Letter 0 Gomes Ferreira Carlos Henrique Academic Editor 2025 Carlos Henrique Gomes Ferreira This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 0

14 Feb 2025

PONE-D-24-24548Estimating affective polarization on a social networkPLOS ONE

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I took over yesterday and carefully reviewed the reviewers' comments.

I believe the article is close to being accepted. One reviewer requested a few additional changes, but I believe they are feasible to implement.

Best,

Carlos

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Reviewers' comments:

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Comments to the Author

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The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #2: Yes

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Reviewer #1: Hohmann & Coscia present a nice paper which introduces a novel measure of affective polarization in social networks. The measure is an extension of their excellent work previously published in Science Advances which introduced a structural measure of polarization but with an added consideration for the presence of interaction hostility. The work has a clear motivation, is technically sound, and makes a strong contribution to the interdisciplinary literature on polarization.

In my opinion, considering the target venue is PLOS One, I am of the opinion that the article should be accepted for publication with minimal delay - all requirements of technical correctness and novelty have been met. For completeness, I offer some thoughts and suggestions below. However, I stress these are largely my opinion and should certainly not be seen as a requirement for publication - the authors can feel free to ignore these points if they disagree.

Thoughts and suggestions

-----------------------------

1. As the authors well know, how to measure polarization is itself a polarizing topic - different research fields approach the problem in different ways. The authors' measure combines that classic affective component, with the structural dimension. However, I think there are many polarization researchers who might argue that social distance (which your measure captures) is not really needed in a measure of AP, it is simply a common symptom. Some people do include the idea of social distance, but most don't, so IMO, it would be best to try to be more explicit about what you are doing. As part of this, I don't think referring to the "structural" component of AP is particularly clear. Rather, I think the framing in terms of social distance offers more clarity. I would perhaps suggest reframing title / abstract to explicitly highlight this novel contribution of your work, e.g. "A social network measure of affective polarization which captures both hostility and social distance". You could also perhaps touch on why researchers may, or may not, want to include these different elements in their measure.

2. You could be bolder in stating the benefits of your approach and possible useful applications.

3. Related to point 1, I would perhaps suggest not to refer to the survey-based approaches as having shortcomings. There is no consensus as to which ingredients of AP must be included in a useful AP measure, and which are optional. In principle, I think many would argue that social distance is not necesarilly a component of AP, despite being correlated. Rather I think your framing may be stronger by talking about your added value instead of the shortcomings of others. Also, what you call the structural component others may refer to as interactional polarization (see your Ref 11 and Yarchi et al. 2021 in Political Communication).

4. I note you refer to other methods which use sentiment, but that you instead use toxicity. I would politely note that at least one of the papers referenced (Ref 11) is also using toxicity, not sentiment as you state.

5. On page 5 you state: "This opinion homophily indicates high structural separation and, therefore, high affective polarization." I understand this argument, but there is plenty of data to suggest that hostile out-group interactions are not so rare (any of the many papers which argue that echo chambers are in fact rare / non-existant). It is very dependent on interaction type (see for example Fig 4 in Mekacher et al. 2023 PNAS Nexus). The measures of social distance typically used are quick high-stakes interactions (e.g., getting married, being neighbors) unlike social media interactions which are low stakes and are therefore more likely to include out-group interactions.

6. You should perhaps briefly note the assumptions underlying your measure's desire for a positive correlation between disagreement and hostility. If by disagreement you mean disagreement in terms of ideological identification that is fine, but that is not necessarily the same as disagreement on actual issues. See for example the papers by Liliana Mason (I Disrespectfully disagree) which discussed how, surprisingly, affective polarization often manifests as substantial hostility between partisan opponents even when those individuals largely *agree* on the details of policy.

7. In your AP measure, any particular reason you chose to equally weight structure and affect?

8. The method validation section could be a little improved in terms of structure. You are using a lot of acronyms which some readers may not be familiar with. You could take a little more time to introduce the other measures and note why they have been used in the past.

9. Personally, I find Fig 2 a bit messy with all the different metrics included in one figure. I'd probably move most of the other metric results to the SI, but its up to you.

10. Lines 274-275. When you talk about ideological labelling, remember to reference the methods section, otherwise we are confused how you have done this.

11. In Figure 5, perhaps consider showing the individual components of the AP measure and then commenting on how the individual components compare to the combined measure.

12. Lines 336 - 337: "These findings align with previous research indicating a consistent upward trend in affective polarization since the 1960s". Statements like this should be precise about exactly which country you are referring to. I note that AP has decreased in many countries! See Boxell & Gentzkow's NBER paper on AP across countries.

Reviewer #2: The online system keep saying "Minimum Character Count Not Met", even if the character count is 3500. I don't know why. Please find the comments for the authors as a separated file attached to this form.

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Submitted filename: review_pone.pdf

 10.1371/journal.pone.0328210.r002 Author response to Decision Letter 1 Submission Version 1

31 Mar 2025

We have included a response to the reviewers in a separate file.

Submitted filename: cover_letter_and_response.pdf

 10.1371/journal.pone.0328210.r003 Decision Letter 1 Gomes Ferreira Carlos Henrique Academic Editor 2025 Carlos Henrique Gomes Ferreira This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 1

16 Jun 2025

PONE-D-24-24548R1Estimating affective polarization on a social networkPLOS ONE

Dear Dr. Hohmann,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

In particular, I would like to thank you for the opportunity to continue the review process of this manuscript. We would like to note that two of the reviewers now consider the article ready for publication.

However, I third reviewer, while acknowledging the authors’ efforts and the lack of consensus in the field, raises an point regarding the conceptual distinction between affective and structural dimensions of polarization.

Although this reviewer ultimately respects the authors’ position, their comments suggest that, at a minimum, the manuscript should explicitly acknowledge this distinction and critically engage with the differing perspectives in the literature.

We kindly ask the authors to consider this in their revision, ensuring that the current framing is clearly justified and that alternative interpretations are adequately addressed.

Please submit your revised manuscript by Jul 31 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Thank you for the opportunity to continue the review process of this manuscript.

We would like to note that two of the reviewers now consider the article ready for publication.

However, a third one, while acknowledging the authors’ efforts and the lack of consensus in the field, raises an point regarding the conceptual distinction between affective and structural dimensions of polarization.

Although this reviewer ultimately respects the authors’ position, their comments suggest that, at a minimum, the manuscript should explicitly acknowledge this distinction and critically engage with the differing perspectives in the literature.

Thus, we kindly ask the authors to consider this in their revision.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Carlos Henrique Gomes Ferreira, Ph.D.

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

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Reviewer #2: Partly

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

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6. Review Comments to the Author

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Reviewer #1: The authors have done an excellent job of responding to all comments. I recommend publication with no further revisions.

Reviewer #2: First, I would like to thank the authors for their effort in addressing my previous concerns. However, I still have concerns regarding the structural aspects analyzed in this work, now referred to as "social distance". While some studies consider this aspect a component or manifestation of affective polarization, others treat it as a distinct dimension of polarization. Personally, I align with the latter perspective and believe that affective and structural dimensions should not be conflated when measuring affective polarization, particularly in the context of social media.

Indeed, social media platforms rely heavily on recommendation algorithms, which significantly shape the structure of interactions by promoting content aligned with users’ interests. In this context, the structural component may represent a mix of social avoidance (which I see as an effect, not a cause, of affective polarization) and algorithmic design.

Even the results presented in Figure 5 could support this interpretation: the affective component appears to precede the structural one. Initially, there are more interactions across communities; however, due to heightened affective polarization, users begin to avoid cross-community engagement, which in turn increases the structural component, or “social distance.”

In my view, the paper would benefit from being reframed as a comparison between these two dimensions of polarization. That said, I respect the authors’ position on the matter and recognize that this remains an open question without a clear consensus in the field.

Reviewer #3: The paper has merit for publication in PLOS ONE. The proposed measure contributes to the research area as an useful method to analyse the factors that drive affective polarization dynamics in online social media platforms.

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Reviewer #2: No

Reviewer #3: No

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 10.1371/journal.pone.0328210.r004 Author response to Decision Letter 2 Submission Version 2

20 Jun 2025

Reviewer #2:

I still have concerns regarding the structural aspects analyzed in this work, now referred to as "social distance''. While some studies consider this aspect a component or manifestation of affective polarization, others treat it as a distinct dimension of polarization. [...] In my view, the paper would benefit from being reframed as a comparison between these two dimensions of polarization. That said, I respect the authors’ position on the matter and recognize that this remains an open question without a clear consensus in the field.

Authors' Answer:

We think the reviewer has a solid point here. We have edited abstract, introduction, and discussion to improve our acknowledgment of this open question -- and to allow the reader siding with the reviewer to still find usefulness in the method we develop by considering exclusively the affective component and relegating the social distance component as a distinct dimension.

Submitted filename: response.pdf

 10.1371/journal.pone.0328210.r005 Decision Letter 2 Gomes Ferreira Carlos Henrique Academic Editor 2025 Carlos Henrique Gomes Ferreira This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 2

30 Jun 2025

Estimating affective polarization on a social network

PONE-D-24-24548R2

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 10.1371/journal.pone.0328210.r006 Acceptance letter Gomes Ferreira Carlos Henrique Academic Editor 2025 Carlos Henrique Gomes Ferreira This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

PONE-D-24-24548R2

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