Betweennesskeskiköinti

Betweennesskeskiköinti is a concept in network analysis describing a variant of node centrality that emphasizes a node’s position near the midpoint of shortest paths between pairs of other nodes. It builds on the idea of betweenness centrality but shifts the focus from merely lying on shortest paths to occupying a central position along those paths.

Formally, in a graph G=(V,E) with distance function dist(.,.), standard betweenness centrality for a node v is B(v) = sum over all s,t in V with s≠t, s≠v, t≠v of σ_st(v)/σ_st, where σ_st is the number of shortest s–t paths and σ_st(v) is the number of those paths that pass through v. Betweennesskeskiköinti introduces a midpoint-focused weight, defining C(v) = sum over s,t as above of w(s,t,v)/σ_st, where w(s,t,v) is larger when dist(s,v) and dist(v,t) are close to each other and near half the total distance dist(s,t). A common choice is w(s,t,v) = exp(-|dist(s,v) − dist(v,t)|/dist(s,t)). Normalization yields a value in [0,1].

Computation of betweennesskeskiköinti follows similar steps to betweenness centrality, using all-pairs shortest paths. One can adapt Brandes-like algorithms to accumulate weights w(s,t,v) instead of the binary indicators. For large networks, approximate methods that sample pairs (s,t) are often employed to reduce computation time.

Applications of betweennesskeskiköinti include identifying bottlenecks and key intermediary actors in social, transportation, and communication networks, as well as exploring how information or goods flow through the network. It provides a complementary perspective to standard betweenness centrality by highlighting nodes that consistently lie near the middle of shortest routes, not just on them. Limitations include sensitivity to network scale, choice of distance metric, and interpretative nuances when networks are sparse or highly modular. See also betweenness centrality and centrality measures.