Statistics on Small Graphs

TL;DR

This paper systematically catalogs small graphs with up to 10 edges and vertices, classifying them by various properties and providing comprehensive counts for each category.

Contribution

It offers the first detailed enumeration and classification tables for small graphs based on multiple standard properties.

Findings

Tables of graph counts in various categories

Classification of small graphs by multiple properties

Comprehensive enumeration data

Abstract

We create the unlabeled or vertex-labeled graphs with up to 10 edges and up to 10 vertices and classify them by a set of standard properties: directed or not, vertex-labeled or not, connectivity, presence of isolated vertices, presence of multiedges and presence of loops. We present tables of how many graphs exist in these categories.