In
graph theory, a
regular graph is a
graph where each vertex has the same number of neighbors; i.e. every vertex has the same
degree or valency. A regular
directed graph must also satisfy the stronger condition that the
indegree and
outdegree of each vertex are equal to each other. A regular graph with vertices of degree
<var >k</var > is called a
<var >k</var >-regular graph or regular graph of degree
<var >k</var >.