TY - JOUR
T1 - A Graph-theoretic perspective on centrality
JO - Social Networks
VL - 28
IS - 4
SP - 466
EP - 484
PY - 2006/10//
T2 -
AU - Borgatti, Stephen P.
AU - Everett, Martin G.
SN - 0378-8733
DO - http://dx.doi.org/10.1016/j.socnet.2005.11.005
UR - http://www.sciencedirect.com/science/article/pii/S0378873305000833
AB - The concept of centrality is often invoked in social network analysis, and diverse indices have been proposed to measure it. This paper develops a unified framework for the measurement of centrality. All measures of centrality assess a node's involvement in the walk structure of a network. Measures vary along four key dimensions: type of nodal involvement assessed, type of walk considered, property of walk assessed, and choice of summary measure. If we cross-classify measures by type of nodal involvement (radial versus medial) and property of walk assessed (volume versus length), we obtain a four-fold polychotomization with one cell empty which mirrors Freeman's 1979 categorization. At a more substantive level, measures of centrality summarize a node's involvement in or contribution to the cohesiveness of the network. Radial measures in particular are reductions of pair-wise proximities/cohesion to attributes of nodes or actors. The usefulness and interpretability of radial measures depend on the fit of the cohesion matrix to the one-dimensional model. In network terms, a network that is fit by a one-dimensional model has a core-periphery structure in which all nodes revolve more or less closely around a single core. This in turn implies that the network does not contain distinct cohesive subgroups. Thus, centrality is shown to be intimately connected with the cohesive subgroup structure of a network.
ER -