indegreev

Indegreev is a term sometimes used in graph theory and programming to denote the indegree of a vertex v in a directed graph. While more common notation uses indegree(v) or indeg(v), indegreev appears as a compact variable name or function in certain texts and codebases, with v treated as the vertex of interest.

Definition and meaning

For a directed graph G = (V,E), the indegree of a vertex v in V is the number of edges that terminate at v. Formally, indegree(v) = |{u in V | (u,v) in E}|. The value indegreev refers to this same quantity when v is specified at the time of notation.

Computation and data structures

Indegree values can be computed by counting incoming edges for each vertex, or by maintaining an in-degree counter for every vertex in data structures such as adjacency lists. In practice, an array indexed by vertex stores indegree values, which can be updated as edges are read or modified. Indegree counts are central to algorithms such as topological sorting, where vertices with indegree 0 are processed first.

Properties and relationships

In a directed graph, the sum of indegree values over all vertices equals the number of edges, |E|. Each indegree is between 0 and |V|−1. Indegree is distinct from out-degree, which counts outgoing edges. In undirected graphs, the term indegree is not used; degree suffices.

Applications and related concepts

Indegree is used in network analysis, graph algorithms, and data processing pipelines. A related notion is in-degree centrality, which measures a vertex’s importance based on the number of incoming connections. indegreev serves as a concise way to reference the specific indegree of vertex v in algorithmic explanations.