nodesthat

In graph theory and network analysis, nodesthat is a term used to denote a subset of nodes that satisfy a given predicate. The term appears in informal literature and in illustrative examples to describe conditional selections within graphs.

Definition: For a directed or undirected graph G = (V, E) and a predicate P: V → {true, false}, the set N = { v ∈ V | P(v) = true } is the nodesthat with respect to P. The nodes in N may induce a subgraph G[N], which has edges among those nodes.

Example predicates include P1(v): degree(v) ≥ k; P2(v): PageRank(v) > α; P3(v) lies on at least one shortest path between two specified nodes. These illustrate how nodesthat can capture different notions of “important” or “relevant” nodes within a graph.

Computation and properties: N can be computed by filtering operations in graph-processing libraries. The nodesthat concept is useful for focused analysis, sampling, or visualization. The choice of predicate affects size and structure; properties such as connectivity, induced subgraph density, and boundary nodes can be analyzed.

See also: Node, Subgraph, Predicate, Filter, Graph.