Generalized entropies and open random and scale-free networks

TL;DR

This paper introduces the concept of open networks and uses Renyi mutual entropies to determine the minimal node set size needed to reliably represent the overall network structure, also identifying key node clusters.

Contribution

It proposes a novel approach to analyze large unknown networks by extrapolating their structure from arbitrary node subsets using entropy measures.

Findings

Minimum critical size of node sets for reliable network representation

Identification of node clusters responsible for network structure

Application of Renyi mutual entropies to open network analysis

Abstract

We propose the concept of open network as an arbitrary selection of nodes of a large unknown network. Using the hypothesis that information of the whole network structure can be extrapolated from an arbitrary set of its nodes, we use Renyi mutual entropies in different q-orders to establish the minimum critical size of a random set of nodes that represents reliably the information of the main network structure. We also identify the clusters of nodes responsible for the structure of their containing network.