Structural Bounds on the Dyadic Effect

TL;DR

This paper establishes tighter bounds on the dyadic effect in complex networks, quantifying how node characteristics influence network topology through dyadicity and heterophilicity.

Contribution

It introduces improved upper bounds and new lower bounds for dyadicity and heterophilicity, refining the feasible region of the dyadic effect in network analysis.

Findings

Bounds are effective in constraining network parameters

Structural arguments improve existing bounds

Computational experiments validate the bounds' usefulness

Abstract

In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to measure how much the assigned characteristic affects the network topology. All possible configurations can be represented in a phase diagram lying in a two-dimensional space that represents the feasible region of the dyadic effect, which is bound by two upper bounds on dyadicity and heterophilicity. Using some network's structural arguments, we are able to improve such upper bounds and introduce two new lower bounds, providing a reduction of the feasible region of the dyadic effect as well as constraining dyadicity and heterophilicity within a specific range. Some computational experiences show the bounds' effectiveness and their usefulness with regards to different classes of networks.