Reinterpreting network measures for models of disease transmission.

In the wake of AIDS and HIV, a better framework is needed to model the pattern of contacts between infectious and susceptible individuals. Several network measures have been defined elsewhere which quantify the distance between 2 nodes, and the centrality of a node, in a network. Stephenson and Zelen (S-Z), however, have recently presented a new measure based on statistical estimation theory and applied it to a network of AIDS cases. This paper shows that the closeness measure proposed by S-Z is equivalent to the effective conductance in an electrical network, fits the measure into the existing theory of percolation, and provides a more efficient algorithm for computing S-Z closeness. The S-Z methodology is compared with the closeness measures of maximal flow, first passage time, and random hitting time. Computational problems associated with the measure are discussed in a closing section.