Alisolmu

Alisolmu, literally “sub-node” in Finnish, is a term used in graph theory and related fields to denote a vertex that lies within a subgraph induced by a subset of vertices of a larger graph. The prefix ali- means sub- or under, and solmu translates to node or knot, giving the basic sense of a subnode. In practice, an ali-solmu is any vertex that belongs to a selected subgraph G[S] where S is a subset of V(G). The term is most common in Finnish-language texts on networks, modular graphs, and hierarchical modeling, though in English-language literature the more common terms are “subnode” or “node within a subgraph.”

Formal definition: Let G = (V,E) be a graph and S ⊆ V. The induced subgraph G[S] has vertex set S and edge set { (u,v) ∈ E : u ∈ S and v ∈ S }. An ali-solmu is any vertex v ∈ S; equivalently, a vertex that lies in the vertex set of a subgraph of G induced by S.

Example: In a graph G with V = {A,B,C,D} and E such that the subgraph induced by S = {B,C} contains the edge B–C, nodes B and C are ali-solmu relative to S.

Uses: Ali-solmu is used when describing properties of network components, such as local degree, subgraph density, and boundary nodes between modules. It supports discussions of modular decomposition and hierarchical clustering, without committing to a single global root.

See also: Graph theory; Subgraph; Induced subgraph; Node; Community detection. Note: the term is not universally standardized; readers encountering ali-solmu should check local terminology in Finnish sources.