A notion of graph likelihood and an infinite monkey theorem

TL;DR

This paper introduces a graph likelihood concept inspired by the infinite monkey theorem, providing algorithms and formulas for certain classes, while leaving computational complexity open.

Contribution

It defines a novel graph likelihood measure and offers algorithms and formulas for specific graph classes, advancing theoretical understanding.

Findings

Defined a graph likelihood measure.

Provided algorithms for certain graph classes.

Identified open problems in computational complexity.

Abstract

We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.