indegA0

indegA0 is a notation used in graph theory to denote the indegree of the vertex A0 in a directed graph G = (V, E). The indegree of A0 is defined as the number of directed edges whose head is A0, i.e., the number of edges of the form (u, A0) in E. If the graph allows parallel edges, each such edge contributes one to indegA0. If self-loops are present, a loop (A0, A0) is typically counted as one toward the indegree of A0, though counting conventions can vary.

In practice, indegA0 is computed by counting all incoming edges to A0 from all other vertices (or from A0 itself if a self-loop exists). For example, in a graph with edges (B, A0), (C, A0), and (D, A0), indegA0 = 3. If the edge (A0, A0) is present, it adds one more to indegA0 under common conventions.

A fundamental property in finite directed graphs is that the sum of the indegrees over all vertices equals the number of edges: sum_{v in V} indeg(v) = |E|. In simple directed graphs without parallel edges or self-loops, each indegree ranges from 0 to |V|−1. IndegA0 is often used in analyses of network structure and dynamics, including measures of node importance and flow where the number of incoming connections matters.

Related concepts include outdegree, the total degree in directed graphs, and indegree centrality, which uses the indegree as a proxy for a node’s influence or visibility within a network. See also directed graphs and adjacency representations for methods to compute indegA0.