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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.