Testing structural balance theories in heterogeneous signed networks

Communications Physics, vol. 7

Abstract

Abstract The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of negative links. This statement, however, can be supported only after a comparison with a benchmark. Since the existing ones disregard actors’ heterogeneity, we extend Exponential Random Graphs to signed networks with both global and local constraints and employ them to assess the significance of empirical unbalanced patterns. We find that the nature of balance crucially depends on the null model: while homogeneous benchmarks favor the weak balance theory, according to which only triangles with one negative link should be under-represented, heterogeneous benchmarks favor the strong balance theory, according to which also triangles with all negative links should be under-represented. Biological networks, instead, display strong frustration under any benchmark, confirming that structural balance inherently characterizes social networks.

Authors 5

1. Anna Gallo

   IMT School for Advanced Studies Lucca · Istituto Nazionale di Alta Matematica Francesco Severi

   Affiliation as printed

   IMT School for Advanced Studies, Piazza San Francesco 19, 55100, Lucca, Italy

   INdAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’, P.le Aldo Moro 5, 00185, Rome, Italy

2. Diego Garlaschelli Aachen Lorentz Institute for Theoretical Physics

   Leiden University · IMT School for Advanced Studies Lucca · Istituto Nazionale di Alta Matematica Francesco Severi

   Affiliation as printed

   IMT School for Advanced Studies, Piazza San Francesco 19, 55100, Lucca, Italy

   INdAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’, P.le Aldo Moro 5, 00185, Rome, Italy

   Lorentz Institute for Theoretical Physics, University of Leiden, Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands

3. Renaud Lambiotte

   University of Oxford

   Affiliation as printed

   Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK

4. Fabio Saracco

   IMT School for Advanced Studies Lucca · Centro Ricerche Enrico Fermi · National Research Council

   Affiliation as printed

   IMT School for Advanced Studies, Piazza San Francesco 19, 55100, Lucca, Italy

   Institute for Applied Computing ‘Mauro Picone’ (IAC), National Research Council, Via dei Taurini 19, 00185, Rome, Italy

   ‘Enrico Fermi’ Research Center (CREF), Via Panisperna 89A, 00184, Rome, Italy

5. Tiziano Squartini corresponding

   IMT School for Advanced Studies Lucca · Istituto Nazionale di Alta Matematica Francesco Severi · University of Amsterdam

   Affiliation as printed

   IMT School for Advanced Studies, Piazza San Francesco 19, 55100, Lucca, Italy

   INdAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’, P.le Aldo Moro 5, 00185, Rome, Italy

   Institute for Advanced Study, University of Amsterdam, Oude Turfmarkt 145, 1012 GC, Amsterdam, The Netherlands

   INdAM-GNAMPA Istituto Nazionale di Alta Matematica 'Francesco Severi', P.le Aldo Moro 5, 00185, Rome, Italy