Reverse engineering of linking preferences from network restructuring

TL;DR

This paper introduces a method to infer the underlying preferences driving network restructuring by analyzing observed edge rewiring, applicable to systems with a single-vertex energy function and detailed balance, validated through simulations and real-world networks.

Contribution

It presents a novel approach to reverse engineer network preferences from restructuring data, linking empirical observations to theoretical energy functions.

Findings

Empirical energies follow a universal function f(k) = -k ln(k).

The method successfully recovers known energies in simulations.

Supports the preferential attachment rule in real networks.

Abstract

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.