BETWEENESS CENTRALITY MEASURES FOR DIRECTED-GRAPHS
WHITE DR,
BORGATTI SP
SOCIAL NETWORKS
16 (4): 335-346 OCT 1994
Abstract:
This paper generalizes
Freeman's geodesic centrality measures for betweenness on undirected graphs to
the more general directed case. Four steps are taken. The point centrality
measure is first generalized for directed graphs. Second, a unique maximally
centralized graph is defined for directed graphs, holding constant the numbers
of points with reciprocatable (incoming and outgoing) versus only
unreciprocatable (outgoing only or incoming only) arcs, and focusing the measure
on the maximally central arrangement of arcs within these constraints.
Alternatively, one may simply normalize on the number of arcs. This enables the
third step of defining the relative betweenness centralities of a point,
independent of the number of points. This normalization step for directed
centrality measures removes Gould's objection that centrality measures for
directed graphs are not interpretable because they lack a standard for
maximality. The relative directed centrality converges with Freeman's
betweenness measure in the case of undirected graphs with no isolates. The
fourth step is to define the measures of this concept of graph centralization in
terms of the dominance of the most central point.
KeyWords Plus:
SOCIAL NETWORKS
Addresses:
WHITE DR, UNIV CALIF IRVINE,IRVINE,CA 92717
UNIV S
CAROLINA,COLUMBIA,SC 29208
Publisher:
ELSEVIER SCIENCE BV, AMSTERDAM