Abstract
Group interactions occur frequently in social settings, yet their properties beyond pairwise relationships in network models remain unexplored. In this work, we study homophily, the nearly ubiquitous phenomena wherein similar individuals are more likely than random to form connections with one another, and define it on simplicial complexes, a generalization of network models that goes beyond dyadic interactions. While some group homophily definitions have been proposed in the literature, we provide theoretical and empirical evidence that prior definitions mostly inherit properties of homophily in pairwise interactions rather than capture the homophily of group dynamics. Hence, we propose a new measure, k-simplicial homophily, which properly identifies homophily in group dynamics. Across 16 empirical networks, k-simplicial homophily provides information uncorrelated with homophily measures on pairwise interactions. Moreover, we show the empirical value of k-simplicial homophily in identifying when metadata on nodes is useful for predicting group interactions, whereas previous measures are uninformative.
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Notes
- 1.
Formally, given \(X^{(k-1)}\) is the \((k-1)\)-skeleton of X, \(\bar{X^{(k-1), k}}\) represents the maximal set of k-simplices which could be added to \(X^{(k-1)}\) while preserving that \(X^{(k-1)} \cup \bar{X^{(k-1), k}}\) is a simplicial complex.
References
Agarwal, S., Mittal, N., Katyal, R., Sureka, A., Correa, D.: Women in computer science research: what is the bibliography data telling us? Acm Sigcas Comput. Soc. 46(1), 7–19 (2016)
Asch, S.E.: Opinions and social pressure. Sci. Am. 193(5), 31–35 (1955)
Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G., Petri, G.: Networks beyond pairwise interactions: structure and dynamics. Phys. Rep. (2020)
Benson, A.R., Abebe, R., Schaub, M.T., Jadbabaie, A., Kleinberg, J.: Simplicial closure and higher-order link prediction. Proc. Nat. Acad. Sci. 115(48), E11221–E11230 (2018)
Brown, R.: Social Psychology. Simon and Schuster (1986)
Dong, Y., Johnson, R.A., Xu, J., Chawla, N.V.: Structural diversity and homophily: a study across more than one hundred big networks. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 807–816 (2017)
Easley, D., Kleinberg, J., et al.: Networks, Crowds, and Markets, vol. 8. Cambridge University Press Cambridge (2010)
Fowler, J.H.: Connecting the congress: a study of cosponsorship networks. Polit. Anal. 14(4), 456–487 (2006)
Fowler, J.H.: Legislative cosponsorship networks in the us house and senate. Soc. Netw. 28(4), 454–465 (2006)
Génois, M., Barrat, A.: Can co-location be used as a proxy for face-to-face contacts? EPJ Data Sci. 7(1), 11 (2018)
Ghrist, R.W.: Elementary Applied Topology, vol. 1. Createspace Seattle (2014)
Hatcher, A.: Algebraic Topology (2002)
Kahle, Matthew, et al.: Topology of random simplicial complexes: a survey. AMS Contemp. Math 620, 201–222 (2014)
Kossinets, G., Watts, D.J.: Empirical analysis of an evolving social network. Science 311(5757), 88–90 (2006)
Kumar, T., Vaidyanathan, S., Ananthapadmanabhan, H., Parthasarathy, S., Ravindran, B.: Hypergraph clustering by iteratively reweighted modularity maximization. Appl. Netw. Sci. 5(1), 1–22 (2020)
Latané, B., Williams, K., Harkins, S.: Many hands make light the work: the causes and consequences of social loafing. J. Personal. Soc. Psychol. 37(6), 822 (1979)
Lazarsfeld, P.F., Merton, R.K., et al.: Friendship as a social process: a substantive and methodological analysis. Freedom Control Modern Soc. 18(1), 18–66 (1954)
McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Ann. Rev. Sociol. 27(1), 415–444 (2001)
Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, pp. 29–42 (2007)
Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)
Ozella, L., Paolotti, D., Lichand, G., Rodríguez, J.P., Haenni, S., Phuka, J., Leal-Neto, O.B., Cattuto, C.: Using wearable proximity sensors to characterize social contact patterns in a village of rural Malawi. EPJ Data Sci. 10(1), 46 (2021)
Satchidanand, S.N., Ananthapadmanaban, H., Ravindran, B.: Extended discriminative random walk: a hypergraph approach to multi-view multi-relational transductive learning. In: Twenty-Fourth International Joint Conference on Artificial Intelligence (2015)
Schaub, M.T., Benson, A.R., Horn, P., Lippner, G., Jadbabaie, A.: Random walks on simplicial complexes and the normalized hodge 1-laplacian. SIAM Rev. 62(2), 353–391 (2020)
Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.-F., Quaggiotto, M., Van den Broeck, W., Régis, C., Lina, B., et al.: High-resolution measurements of face-to-face contact patterns in a primary school. PloS One 6(8), e23176 (2011)
Veldt, N., Benson, A.R., Kleinberg, J.: Higher-order homophily is combinatorially impossible (2021). arXiv:2103.11818
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Sarker, A., Northrup, N., Jadbabaie, A. (2023). Generalizing Homophily to Simplicial Complexes. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_24
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