Abstract
Defining accurate models for real-world social networks is essential across various research fields including sociology, epidemiology, and marketing. Such models serve as indispensable tools to capture the dynamics of phenomena ranging from disease spread to rumor dissemination, encapsulating intricate patterns of interactions among individuals within a population. To this end, a latent geometry and/or hidden degrees can be used to obtain networks that are small-world, highly clustered, and have a scale-free degree distributions.
This study aims to integrate group mixing within the framework of latent geometry models. Our approach is based on conceptualizing a graph with a planted partition as the union of different mono- and bipartite subgraphs, for intra- and inter-block edges, respectively. We highlight that the hidden degree – the analogous of the radial coordinate in purely geometric hyperbolic models – must be replaced by a hidden fitness, and that all latent features must be assigned to the nodes once and for all, rather than once for each subgraph.
Through extensive simulations, we show that the proposed model generates networks with a unique combination of features, that cannot be obtained with standard geometric models nor with maximum entropy degree-corrected block models.
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References
Keeling, M.: The implications of network structure for epidemic dynamics. Theor. Popul. Biol. 67(1), 1–8 (2005)
Ribeiro, H.V., Sunahara, A.S., Sutton, J., Perc, M., Hanley, Q.S.: City size and the spreading of COVID-19 in Brazil. PLoS ONE 15(9), e0239699 (2020)
Colizza, V., Barrat, A., Barthélemy, M., Vespignani, A.: The role of the airline transportation network in the prediction and predictability of global epidemics. Proc. Natl. Acad. Sci. 103(7), 2015–2020 (2006)
Newman, M.: Networks. Oxford University Press, Oxford (2018)
Cimini, G., Squartini, T., Saracco, F., Garlaschelli, D., Gabrielli, A., Caldarelli, G.: The statistical physics of real-world networks. Nat. Rev. Phys. 1(1), 58–71 (2019)
Serrano, M.A., Krioukov, D., Boguná, M.: Self-similarity of complex networks and hidden metric spaces. Phys. Rev. Lett. 100(7), 078701 (2008)
Squartini, T., Garlaschelli, D.: Analytical maximum-likelihood method to detect patterns in real networks. New J. Phys. 13(8), 083001 (2011)
Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Boguná, M.: Hyperbolic geometry of complex networks. Phys. Rev. E 82(3), 036106 (2010)
Krioukov, D.: Clustering implies geometry in networks. Phys. Rev. Lett. 116, 208302 (2016)
Serrano, M.A., Boguná, M.: The shortest path to network geometry: a practical guide to basic models and applications, elements in structure and dynamics of complex networks. Camb. Univ. Press Camb. Engl. 10, 9781108865791 (2022)
Boguna, M., Bonamassa, I., De Domenico, M., Havlin, S., Krioukov, D., Serrano, M.: Network geometry. Nat. Rev. Phys. 3(2), 114–135 (2021)
Désy, B., Desrosiers, P., Allard, A.: Dimension matters when modeling network communities in hyperbolic spaces. PNAS Nexus 2(5), pgad136 (2023)
Kertész, J., Török, J., Murase, Y., Jo, H.-H., Kaski, K.: Modeling the complex network of social interactions. In: Rudas, T., Péli, G. (eds.) Pathways Between Social Science and Computational Social Science. CSS, pp. 3–19. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-54936-7_1
McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27(1), 415–444 (2001)
Karrer, B., Newman, M.E.J.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83, 016107 (2011)
Peixoto, T.P.: Hierarchical block structures and high-resolution model selection in large networks. Phys. Rev. X 4, 011047 (2014)
Fronczak, P., Fronczak, A., Bujok, M.: Exponential random graph models for networks with community structure. Phys. Rev. E 88, 032810 (2013)
Park, J., Newman, M.E.J.: Statistical mechanics of networks. Phys. Rev. E 70(6), 066117 (2004)
Robins, G., Snijders, T., Wang, P., Handcock, M., Pattison, P.: Recent developments in exponential random graph (p*) models for social networks. Soc. Netw. 29(2), 192–215 (2007)
Garlaschelli, D., Loffredo, M.I.: Fitness-dependent topological properties of the world trade web. Phys. Rev. Lett. 93(18), 188701 (2004)
Bernaschi, M., Celestini, A., Guarino, S., Mastrostefano, E., Saracco, F.: The fitness-corrected block model, or how to create maximum-entropy data-driven spatial social networks. Sci. Rep. 12(1), 18206 (2022)
Kitsak, M., Papadopoulos, F., Krioukov, D.: Latent geometry of bipartite networks. Phys. Rev. E 95, 032309 (2017)
Alstott, J., Bullmore, E., Plenz, D.: PowerLaw: a python package for analysis of heavy-tailed distributions. PLoS ONE 9(1), e85777 (2014)
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Guarino, S., Mastrostefano, E., Torre, D. (2024). The Hidden-Degree Geometric Block Model. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1143. Springer, Cham. https://doi.org/10.1007/978-3-031-53472-0_34
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