nodessuch

nodessuch is a theoretical construct in graph theory and formal logic intended to denote the subset of nodes in a graph that satisfy a given predicate. In informal notation it is often written as nodessuch(G, P). In standard set-builder notation this corresponds to { v ∈ V(G) | P(v) }.

Use and interpretation: nodessuch defines an induced subgraph when used to select nodes; the edges among them form the induced subgraph G[S]. The predicate P can express properties like degree, label, distance, or other attributes. The operator is not part of a single formal language but appears in pedagogical materials and discussions about graph querying and node-based filtering.

Examples: In a social network G = (V,E), nodessuch(G, deg(v) > 5) yields { v ∈ V | deg(v) > 5 }. If P(v) = "type = server", then S = nodessuch(G, P); the induced subgraph G[S] contains all server nodes and the edges between them.

Relation and alternatives: Similar ideas appear as vertex subset selection, graph filters, or queries in languages such as Cypher, SPARQL, and GraphQL, where predicates select nodes or vertices based on attributes and relations.

History and notes: nodessuch is not a standardized term in formal graph theory. It is primarily found in didactic explanations, informal discussions, or as a placeholder in examples to illustrate how node-based predicates restrict attention to a subset of a graph. See also: vertex subset, induced subgraph, graph query languages, node predicate.