Proper network randomization is key to assessing social balance

Abstract

Social ties, either positive or negative, lead to signed network patterns, the subject of balance theory. For example, strong balance introduces cycles with even numbers of negative edges. The statistical significance of such patterns is routinely assessed by comparisons to null models. Yet, results in signed networks remain controversial. Here, we show that even if a network exhibits strong balance by construction, current null models can fail to identify it. Our results indicate that matching the signed degree preferences of the nodes is a critical step and so is the preservation of network topology in the null model. As a solution, we propose the STP null model, which integrates both constraints within a maximum entropy framework. STP randomization leads to qualitatively different results, with most social networks consistently demonstrating strong balance in three- and four-node patterns. On the basis our results, we present a potential wiring mechanism behind the observed signed patterns and outline further applications of STP randomization.

Percolation of conditional dependency clusters based on edge-coupled interdependent networks

“…S A and S B are monotonically increasing functions with respect to R A and R B from equation (7), so the values of R A and R B determine the values of GC for networks A and B. The two curves do not intersect and the values of ( ) a = á ñ = = .…”

“…Numerous complex systems in reality life can be represented as networks, such as the power network, transportation network, economic network, etc [1][2][3][4][5][6][7]. These networks bring convenience to people's lives, while their complexity is also increasing, and the networks' resistance to disruption is of extensively concerned [8,9].…”