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A Heterophily-Based Polarization Measure for Multi-community Networks

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Social Informatics (SocInfo 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13618))

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Abstract

This work proposes a heterophily-based metric for quantifying polarization in social networks where multiple ideological, antagonistic communities coexist. This metric captures node-level polarization and is built on user’s affinity towards other communities rather than their own. Node-level values can then be aggregated at the community, network, or sub-network level, providing a more detailed map of polarization. We tested our metric on the Polblogs network, White Helmets Twitter interaction network with two communities and the VoterFraud2020 domain network with five communities. We also tested our metric on dK-random graphs to verify that it results in low polarization scores, as expected. Finally, we compared our metric with two widely used polarization measures: Guerra’s polarization index and RWC.

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References

  1. Media Bias/Fact Check News. https://mediabiasfactcheck.com/. Accessed 25 July 2022

  2. Abilov, A., Hua, Y., Matatov, H., Amir, O., Naaman, M.: Voterfraud 2020: a multi-modal dataset of election fraud claims on Twitter. In: ICWSM (2021)

    Google Scholar 

  3. Adamic, L.A., Glance, N.: The political blogosphere and the 2004 U.S. election: Divided they blog. In: Proceedings of the 3rd International Workshop on Link Discovery, LinkKDD 2005, pp. 36–43. Association for Computing Machinery, New York (2005)

    Google Scholar 

  4. Belcastro, L., Cantini, R., Marozzo, F., Talia, D., Trunfio, P.: Learning political polarization on social media using neural networks. IEEE Access 8, 47177–47187 (2020)

    Article  Google Scholar 

  5. Borge-Holthoefer, J., Magdy, W., Darwish, K., Weber, I.: Content and network dynamics behind egyptian political polarization on Twitter. In: Proceedings of the 18th ACM Conference on Computer Supported Cooperative Work & Social Computing, pp. 700–711 (2015)

    Google Scholar 

  6. Conover, M., Ratkiewicz, J., Francisco, M., Gonçalves, B., Menczer, F., Flammini, A.: Political polarization on Twitter. In: Fifth International AAAI Conference on Weblogs and Social Media, January 2011

    Google Scholar 

  7. Darwish, K.: Quantifying polarization on twitter: the kavanaugh nomination. In: Weber, I., Darwish, K.M., Wagner, C., Zagheni, E., Nelson, L., Aref, S., Flöck, F. (eds.) SocInfo 2019. LNCS, vol. 11864, pp. 188–201. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34971-4_13

    Chapter  Google Scholar 

  8. Demszky, D., Garg, N., Voigt, R., Zou, J.Y., Gentzkow, M., Shapiro, J.M., Jurafsky, D.: Analyzing polarization in social media: Method and application to tweets on 21 mass shootings. In: NAACL (2019)

    Google Scholar 

  9. DiMaggio, P., Evans, J., Bryson, B.: Have American’s social attitudes become more polarized? Am. J. Sociol. 102(3), 690–755 (1996)

    Article  Google Scholar 

  10. Emamgholizadeh, H., Nourizade, M., Tajbakhsh, M.S., Hashminezhad, M., Esfahani, F.N.: A framework for quantifying controversy of social network debates using attributed networks: biased random walk (brw). Soc. Netw. Anal. Min. 10, 1–20 (2020)

    Article  Google Scholar 

  11. Esteban, J., Ray, D.: On the Measurement of Polarization. Econometrica 62(4), 819–851 (1994)

    Article  Google Scholar 

  12. Friedkin, N.E.: Horizons of observability and limits of informal control in organizations. Soc. Forces 62(1), 54–77 (1983)

    Article  Google Scholar 

  13. Garimella, K., Morales, G., Gionis, A., Mathioudakis, M.: Quantifying controversy in social media. ACM Trans. Soc. Comput. 1, May 2015

    Google Scholar 

  14. Guerra, P.H.C., Meira, W., Cardie, C., Kleinberg, R.D.: A measure of polarization on social media networks based on community boundaries. In: ICWSM (2013)

    Google Scholar 

  15. Lozares, C., Verd, J.M., Cruz, I., Barranco, O.: Homophily and heterophily in personal networks. from mutual acquaintance to relationship intensity. Quality & Quantity 48, September 2014

    Google Scholar 

  16. Mahadevan, P., Krioukov, D., Fall, K., Vahdat, A.: Systematic topology analysis and generation using degree correlations. ACM SIGCOMM Computer Communication Review 36, June 2006

    Google Scholar 

  17. Morales, A.J., Borondo, J., Losada, J.C., Benito, R.M.: Measuring political polarization: Twitter shows the two sides of Venezuela. Chaos: Interdisciplinary J. Nonlinear Sci. 25(3), 033114 (2015)

    Google Scholar 

  18. Nair, S., Iamnitchi, A.: The polarized web of the voter fraud claims in the 2020 US presidential election. In: Workshop Proceedings of the 15th International AAAI Conference on Web and Social Media. International Workshop on Social Sensing (2021)

    Google Scholar 

  19. Nair, S., Ng, K., Iamnitchi, A., Skvoretz, J.: Diffusion of social conventions across polarized communities: an empirical study. Social Network Analysis and Mining 11, December 2021

    Google Scholar 

  20. Salloum, A., Chen, T.H.Y., Kivelä, M.: Separating polarization from noise: comparison and normalization of structural polarization measures. In: Proceedings of the ACM on Human-Computer Interaction 6(CSCW1), April 2022

    Google Scholar 

  21. Yang, M., Wen, X., Lin, Y.R., Deng, L.: Quantifying content polarization on Twitter. In: 2017 IEEE 3rd International Conference on Collaboration and Internet Computing (CIC), pp. 299–308 (2017)

    Google Scholar 

  22. Ortiz de Zarate, J., Di Giovanni, M., Feuerstein, E., Brambilla, M.: Measuring Controversy in Social Networks Through NLP, pp. 194–209. Springer International Publishing (09 2020)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of South Florida, Tampa, USA

    Sreeja Nair

  2. Maastricht University, Maastricht, Netherlands

    Adriana Iamnitchi

Authors
  1. Sreeja Nair
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  2. Adriana Iamnitchi
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Corresponding author

Correspondence to Sreeja Nair .

Editor information

Editors and Affiliations

  1. Universität Koblenz-Landau, Koblenz, Germany

    Frank Hopfgartner

  2. National University of Singapore, Singapore, Singapore

    Kokil Jaidka

  3. GESIS – Leibniz-Institut für Sozialwissenschaften, Cologne, Germany

    Philipp Mayr

  4. University of Glasgow, Glasgow, UK

    Joemon Jose

  5. University of Glasgow, Glasgow, UK

    Jan Breitsohl

Appendix A Additional Materials

Appendix A Additional Materials

1.1 A.1 Edge Distribution of VoterFraud2020 Domain Network

Figure 1 depicts the distribution of edges to communities after relabelling unknown based on the dominant label in the node’s direct neighborhood. The majority of the edges in the right community are to themselves. Left-center also has most of its edges to left-center and right.

Fig. 1.
figure 1

Heatmap of the edge distribution between communities in the VoterFraud2020 domain network with five communities: left, left-center, center, right-center, right.

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Fig. 2.
figure 2

(a) The Polblogs interaction network: light green represents liberal nodes, and red represents conservative; (b) The White Helmets Twitter network. The colors red represents anti-White Helmets and green represents pro-White Helmets; (c) The VoterFraud2020 domain network, with colors reflects the node’s political orientation: red for right, orange for right-center, yellow for center, green for left-center and blue for left.

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Fig. 3.
figure 3

(a) The Polblogs network colored based on cross-community affinity (b) The White Helmets Twitter colored based on cross-community affinity. (c) The VoterFraud2020 domain network colored based on cross-community affinity. The darker the color, the lower the value, thus higher polarization.

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1.2 A.2 Visual Representation of Datasets

Polblogs. Figure 2a shows the visualization of Polblogs community structure. Light green represents liberal and red represents conservative. Figure 3a displays the Polblogs network colored based on the cross-community affinity of each node. The greater the value, the lighter the shade. Different nodes have distinct hues, which demonstrates that their values vary. The figure is dominated by a darker hue, indicating that the majority of nodes have low cross-community affinity values, resulting in a polarized network.

White Helmets Twitter Interaction Network. Figure 2b depicts the visual representation of communities in the WhiteHelmet interaction network. The colors red represents anti-White Helmets and green represents pro-White Helmets. Figure 3b displays the White Helmets network colored based on the cross-community affinity of each node. The greater the value, the lighter the shade. The figure is dominated by a darker hue, indicating a polarized network.

VoterFraud2020 Domain Network. The visual representation of communities in the network is shown in Fig. 2c. The color reflects the political orientation of the nodes, with red for right, orange for right-center, yellow for center, green for left-center, and blue for left. The right (47.4%) and the left-center (35.5%) constitute the majority of the network. The center has 7.4% nodes, the left has 6.1%, and the right-center has 3.6% nodes. Figure 3c shows the VoterFraud2020 domain network colored based on nodes’ cross-community affinity value. Darker hue means low cross-community affinity. Overall, the graph shows darker shade indicating that the network is polarization.

1.3 A.3 Scenarios of Network for CCA Calculation

Figure 4 depicts various scenarios of a network with seven nodes and two communities: red and green. For each scenario, the cross-community affinity for node v is provided. In scenario Fig. 4a all the immediate neighbors and two-hop neighbors of node v are members of the same community, indicating the absence of cross-community affinity. In this instance, CCA(v) has a value of -1.5. Similarly, in scenario Fig. 4f, all neighbors inside a two-hop neighborhood belong to the opposing community, resulting in a node with maximum cross-community affinity, where, CCA(v) equals 1.5. CCA(v) = 0 in the Fig. 4d, because the neighborhood of node v is equally distributed among both communities.

Fig. 4.
figure 4

Different scenario of a network with 7 nodes and two communities: red and green. The cross-community affinity of node v, CCA(v) is shown. (Color figure online)

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1.4 A.4 Ideological Distance for Five Communities

Table 3 shows the distance between communities in a scenario in which we consider \(C=5\). Right and left communities are on the ends of the spectrum. As a result, the distance between them is 1.

Table 3. The ideological distance between 5 communities for VoterFraud2020 domain network
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1.5 A.5 Relabelling VoterFraud2020 Domain Network

We randomized the labeling of the nodes of VoterFraud2020 domain network to see the effect on the polarization metric. We relabelled the network in three ways. In the first case, we randomly relabelled “unknown” without altering the community size of labeled nodes. We determined the number of “unknown” required by each community to maintain the community sizes. Then, “unknown” was arbitrarily assigned to each community. Even though we relabel “unknown” only, 75.6% of nodes in the network are “unknown”, making the network at least 75% random.

In the second case, we relabelled all the nodes in the network randomly but kept the number of nodes in each community the same as in the original VoterFraud2020 domain network. In the third case, the five labels are equally distributed to the network, thus creating five equal-sized communities. These random labeling are performed 10 times, and the results provided are averaged over these outcomes. The polarization scores for these experiments are given in Table 4. The left-center community score in the experiment where “unknown” labels are randomly assigned shows that the community is polarized, indicating that this network is not totally random. The network had negative polarization values in all randomization experiments, indicating a lack of polarization.

Table 4. Community-level and network-level polarization score for VoterFraud2020 domain network with different labellings of unknown nodes.
Full size table

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Nair, S., Iamnitchi, A. (2022). A Heterophily-Based Polarization Measure for Multi-community Networks. In: Hopfgartner, F., Jaidka, K., Mayr, P., Jose, J., Breitsohl, J. (eds) Social Informatics. SocInfo 2022. Lecture Notes in Computer Science, vol 13618. Springer, Cham. https://doi.org/10.1007/978-3-031-19097-1_32

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  • DOI: https://doi.org/10.1007/978-3-031-19097-1_32

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