A graph with a finite number of nodes and edges. If it has 
nodes and has no multiple edges
or graph loops (i.e., it is simple),
it is a subgraph of the complete
graph 
.
A graph which is not finite is called infinite. If every node has finite degree, the graph is called locally finite. The Cayley graph of a group with respect to a finite generating set is always locally finite, even if the group itself is infinite.
See also
Cubical Graph, Cycle Graph, de Bruijn Graph, Dodecahedral Graph, Grid Graph, Hanoi Graph, Harary Graph, Hoffman-Singleton Graph, Icosahedral Graph, Moore Graph, Null Graph, Octahedral Graph, Odd Graph, Petersen Graph, Platonic Graph, Polyhedral Graph, Schlegel Graph, Singleton Graph, Star Graph, Tetrahedral Graph, Thomassen Graphs, Turán Graph, Tutte Graph, Triangular Graph, Wheel Graph
This entry contributed by Margherita Barile
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Cite this as:
Barile, Margherita. "Finite Graph." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FiniteGraph.html