The in-degree of an undirected graph is the number of edges incident to each vertex:

Self-loops are counted twice:

Undirected graphs correspond to directed graphs with each edge both an in- and out-edge:

For an undirected graph, the vertex in-degree and out-degree are equal to the vertex degree:

For a directed graph, the sum of the vertex in-degree and out-degree is the vertex degree:

Put the vertex degree, in-degree, and out-degree before, above, and below the vertex, respectively:

The sum of the in-degrees of all vertices of an undirected graph is twice the number of edges:

The sum of the in-degrees of all vertices of a directed graph is equal to the number of edges:

The vertex in-degrees of an undirected graph can be obtained from the adjacency matrix:

The vertex in-degrees of a directed graph can be obtained from the adjacency matrix:

The vertex in-degrees for an undirected graph can be obtained from the incidence matrix:

A connected directed graph is Eulerian iff every vertex has equal in-degree and out-degree: