Finite graph

A graph-vertex-edge $G=(V,E)$ is finite if its vertex set $V$ is finite. For a simple graph, this implies $E$ is finite as well.

If $|V|=n$ and $|E|=m$, then for a simple undirected graph,

Handshaking identity (useful fact). For a finite simple undirected graph,

Finite graphs are the basic setting for many combinatorial arguments and algorithms, and they often arise as finite subgraphs of infinite graphs (for example, finite regions of the lattice lattice-zd ).