InOutDegree

InOutDegree is a term used in graph theory and network analysis to describe the in-degree and out-degree of a node in a directed graph. It is usually represented as a two-element vector or pair (din(v), dout(v)) for a vertex v.

For a directed graph G = (V, E), the in-degree din(v) is the number of edges that terminate at v, while the out-degree dout(v) is the number of edges that originate from v. A self-loop on v contributes one to both din(v) and dout(v). The total degree of v is often defined as deg(v) = din(v) + dout(v), though this is separate from the InOutDegree pair.

The InOutDegree of a node provides a compact summary of its connectivity and role within the network. Nodes with high dout but low din may act as sources or broadcasters, while those with high din and low dout may function as sinks or receivers. Nodes with roughly balanced in- and out-degrees can serve as intermediaries in information or transaction flows. Visualizations frequently plot din(v) against dout(v) to reveal patterns in network structure.

InOutDegree is used in various analyses, including centrality calculations, clustering and community detection, and modeling of diffusion processes. It also serves as a simple feature for machine learning tasks on graphs, such as node classification or anomaly detection. Related concepts include the total degree, degree distributions, and local neighborhood statistics, all of which complement the information provided by the InOutDegree pair.