Vertex routing models

TL;DR

This paper introduces vertex routing models to analyze information flow in networks, highlighting how memory traces influence global properties and the distribution of attractors, with implications for social network analysis.

Contribution

It proposes a new class of routing models incorporating memory effects and characterizes their long-term behavior and attractor distributions.

Findings

Number of vertices with non-zero centrality varies with memory presence

Distribution of cycle lengths shows scaling collapse in the thermodynamic limit

Memory traces significantly affect the structure of information flow

Abstract

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.