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Snarks
A snark is a connected bridgeless cubic graph (i.e., a biconnected cubic graph) with edge chromatic number of four (i.e. it cannot be properly edgecoloured using 3 colours). The census lists all snarks up to the order 30 and was provided by The House of Graphs (source).

Cubic graphs
This collection contains a complete census of connected cubic graphs of order at most 20. The data was prepared by Gordon Royle(source) and later extended at the House of Graphs (source).

Strongly regular graphs
A kregular simple graph G on nu nodes is strongly kregular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a regular graph), every adjacent pair of vertices has lambda common neighbors, and every nonadjacent pair has mu common...

Networks
Network theory is the study of graphs as a representation of either symmetric or asymmetric relations between discrete objects. It studies technological networks (the internet, power grids, telephone networks, transportation networks), social networks (social graphs, affiliation networks),...

Class 2 graphs
Vizing's theorem states that a graph can be edgecoloured in either d or d+1 colours, where d is the maximum degree of the graph. This partitions graphs into two classes, with the ones requiring d+1 colours known as class 2 graphs. The following collection was calculated by Gordon Royle (source)...