connectionssome

Connectionssome is a term used in network analysis to describe a measurement of how many connections a given node has to a specified subset of other nodes, rather than to the entire network. The name blends "connections" with the word "some" to emphasize partial, predicate-based connectivity. In practice, connectionssome helps distinguish between generic degree and connectivity to a targeted group or property.

Formal definition: Given a graph G = (V,E) and a target subset S ⊆ V defined by a predicate, the connectionssome of a node v ∈ V is c(v,S) = |N(v) ∩ S|, where N(v) is the set of neighbors of v. A normalized version, c′(v,S) = c(v,S)/|S|, expresses the proportion of the target set that connects to v. Some literature uses a boolean variant indicating whether c(v,S) > 0.

Applications: Connectionssome is used to analyze community overlap, reach within a subgroup, or influence in networks where the relevance of connections depends on belonging to a defined set (such as a demographic, interest group, or functional role). It complements degree and clustering measures by focusing on a defined subset rather than all neighbors.

Limitations and alternatives: The concept depends on the choice of subset S and predicates, which can introduce bias if S is poorly defined. It is often used alongside other metrics such as degree, betweenness, or modularity to provide a more complete view of network structure. In some cases, the term is used informally in software documentation as a variable name or feature description.