  This paper describes a novel approach to modeling homphily, i.e. the tendency
of nodes that share (or differ in) certain attributes to be linked; we consider
dynamic networks in which nodes can be added over time but not removed. Our
application is to HIV genetic linkage analysis that has been used to
investigate HIV transmission dynamics. In this setting, two HIV sequences from
different persons with HIV (PWH) are said to be linked if the genetic distance
between these sequences is less than a given threshold. Such linkage suggests
that that the nodes representing the two infected PWH, are close to each other
in a transmission network; such proximity would imply that either one of the
infected people directly transmitted the virus to the other or indirectly
transmitted it through a small number of intermediaries. These viral genetic
linkage networks are dynamic in the sense that, over time, a group or cluster
of genetically linked viral sequences may increase in size as new people are
infected by those in the cluster either directly or through intermediaries. Our
approach makes use of a logistic model to describe homophily with regard to
demographic and behavioral characteristics that is we investigate whether
similarities (or differences) between PWH in these characteristics impacts the
probability that their sequences are be linked. Such analyses provide
information about HIV transmission dynamics within a population.
