outdegvD1

OutdegvD1 is a compact notation used in graph theory to denote the out-degree of a specific vertex D1 in a directed graph. In a directed graph G = (V, E), the out-degree of a vertex v ∈ V is the number of edges that originate at v, i.e., the count of arcs (v, w) ∈ E for which w ∈ V. When D1 is the vertex in question, outdegvD1 refers to deg+(D1) or outdeg(D1).

Notation and interpretation may vary by text. While many authors write deg+(D1) or outdeg(D1), some informal notes use outdegvD1 as a shorthand for the same quantity. The essential meaning is the number of immediate successors of D1 in the digraph.

Computation is straightforward: examine all directed edges leaving D1 and count them. For example, if E contains (D1, D2), (D1, D3), and (D2, D1), then outdegvD1 = 2 because D1 has two outgoing edges to D2 and D3.

Properties are standard for out-degree. The out-degree is a nonnegative integer. The sum of the out-degrees over all vertices equals the total number of arcs in the digraph. In a simple digraph with n vertices, the out-degree of any vertex satisfies deg+(v) ≤ n − 1.

Applications include analyses of network structure, algorithms for random walks, and processes that depend on the availability of outgoing edges. Outdeg concepts complement in-degree measures and are often used in constructing degree sequences and in threshold-based graph processes.