An evolutionary game approach for determination of the structural conflicts in signed networks.

Shaolin Tan,Jinhu Lü

doi:10.1038/srep22022

Abstract

Social or biochemical networks can often divide into two opposite alliances in response to structural conflicts between positive (friendly, activating) and negative (hostile, inhibiting) interactions. Yet, the underlying dynamics on how the opposite alliances are spontaneously formed to minimize the structural conflicts is still unclear. Here, we demonstrate that evolutionary game dynamics provides a felicitous possible tool to characterize the evolution and formation of alliances in signed networks. Indeed, an evolutionary game dynamics on signed networks is proposed such that each node can adaptively adjust its choice of alliances to maximize its own fitness, which yet leads to a minimization of the structural conflicts in the entire network. Numerical experiments show that the evolutionary game approach is universally efficient in quality and speed to find optimal solutions for all undirected or directed, unweighted or weighted signed networks. Moreover, the evolutionary game approach is inherently distributed. These characteristics thus suggest the evolutionary game dynamic approach as a feasible and effective tool for determining the structural conflicts in large-scale on-line signed networks.

Highlights

Social or biochemical networks can often divide into two opposite alliances in response to structural conflicts between positive and negative interactions
A signed network can be denoted by a graph G = (V, E) with V = {v1, v2, ..., vN} representing the nodes and E = {eij|i, j = 1, 2,..., N} the edges, where eij = 1, − 1, or 0 indicate a positive edge, a negative edge, or no edge between nodes vi and vj, respectively
After imposing the proposed evolutionary game dynamics on the above signed networks, we find that all the nodes adaptively adjust their strategies to gain better fitness

Summary

Introduction

Social or biochemical networks can often divide into two opposite alliances in response to structural conflicts between positive (friendly, activating) and negative (hostile, inhibiting) interactions. An evolutionary game dynamics on signed networks is proposed such that each node can adaptively adjust its choice of alliances to maximize its own fitness, which yet leads to a minimization of the structural conflicts in the entire network. The evolutionary game approach is inherently distributed These characteristics suggest the evolutionary game dynamic approach as a feasible and effective tool for determining the structural conflicts in large-scale on-line signed networks. A signed network is structurally balanced if and only if all its cycles have an even number of negative edges. The minimal numbers of edges, which should be deleted to make the network balanced, are called structural conflicts of the signed network. As a consequence, distributed heuristic approaches, which allow agents themselves www.nature.com/scientificreports/

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