Maximizing Entropy Yields Spatial Scaling in Social Networks

TL;DR

This paper explains the universal spatial scaling law in social networks as a consequence of individuals maximizing their friendship diversity through entropy maximization, revealing a fundamental principle behind social spatial structure.

Contribution

It introduces an entropy-based model that accounts for the observed universal spatial scaling law in social networks, linking social behavior to information theory.

Findings

The probability density of friendships at distance r scales as r^{-1}.

Maximizing information entropy explains the spatial distribution of social ties.

The model suggests individuals benefit from diverse social connections.

Abstract

In addition to the well known common properties such as small world and community structures, recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $r$ scales as $P(r)\propto r^{-1}$. The basic principle that yields this spatial scaling property is not yet understood. Here we propose a fundamental origin for this law based on the concept of entropy. We show that this spatial scaling law can result from maximization of information entropy, which means individuals seek to maximize the diversity of their friendships. Such spatial distribution can benefit individuals significantly in optimally collecting information in a social network.