On the complexity of graphs (networks) by information content, and conditional (mutual) information given other graphs

TL;DR

This paper explores the information content of graphs, including conditional information given background graphs, introduces an estimation algorithm, and demonstrates its application on chemical compound graphs.

Contribution

It presents a novel algorithm for estimating the information content of graphs conditioned on background graphs, with practical examples.

Findings

Algorithm effectively estimates graph information content

Conditional information varies significantly with background graphs

Application to chemical compounds demonstrates practical utility

Abstract

This report concerns the information content of a graph, optionally conditional on one or more background, "common knowledge" graphs. It describes an algorithm to estimate this information content, and includes some examples based on chemical compounds.