Filtering Statistics on Networks

TL;DR

This paper investigates how filtering simple patterns on various networks affects information processing, revealing that random graphs exhibit richer filtering statistics than deterministic ones, influenced mainly by graph structure and degree.

Contribution

It provides exact solutions for simple filter patterns and compares filtering statistics across different network architectures, highlighting the impact of randomness and degree.

Findings

Filtering in random graphs yields richer statistics than deterministic graphs.

Graph structure and vertex degree primarily determine filtering statistics.

Increasing vertex degree reduces the statistical richness of filtering.

Abstract

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph's degree.