Erratum: Betweenness Centralization for Bipartite Graphs

In the article by Philip Sinclair, “Betweenness Centralization for Bipartite Graphs,” published in The Journal of Mathematical Sociology, Volume 29, Number 1, January–March 2005, pages 25–31.

Theorem 3 is correct for connected graphs and should read:

Theorem 3

Let G be a connected graph. Then

For graphs that are not necessarily connected the following theorem holds.

Theorem 4

Let G be a graph with components C ₁,…, C _p . Then

where n _i  = |V(C _i )|, for 1 ≤ i ≤ p.

Proof 1

In a similar fashion to the proof of Theorem 3, we have for a component C _t of G that,

So

Hence,