Emergence of a Mutual-Growth Mechanism in Networks Evolved by Social Preference Based on Indirect Utility

Abstract

Abstract Preferential attachment is an important mechanism in the structural evolution of complex networks. However, though the resources of a network have an effect beyond a direct relationship, growth by preferential attachment based on indirect resources has not been systematically investigated. Here, we propose a mathematical model that reflects the utility of direct and indirect resources to the preference. Our analysis showed that preferential attachment involving indirect utility forms a converged and hierarchical structure, thereby significantly increasing the indirect utility across the entire network. Further, we found that the structures are formed by mutual growth between adjacent nodes, which promotes a scaling exponent of 1.5 between the number of indirect and direct links. Lastly, by examining several real networks, we found evidence of mutual growth, especially in social networks. Overall, our findings demonstrate the role of preference by indirect utility in the structural and functional evolution of large-scale social networks.