Social network analysis and shared-patient physician networks have become effective ways of studying physician collaborations. Assortative mixing or "homophily" is the network phenomenon whereby the propensity for similar individuals to form ties is greater than for dissimilar individuals. Motivated by the public health concern of risky-prescribing among older patients in the United States, we develop network models and tests involving novel network measures to study whether there is evidence of geographic homophily in prescribing and deprescribing in the specific shared-patient network of physicians linked to the US state of Ohio in 2014. Evidence of homophily in risky-prescribing would imply that prescribing behaviors help shape physician networks and could inform interventions to reduce risky-prescribing (e.g., should interventions target groups of physicians or select physicians at random). Furthermore, if such effects varied depending on the structural features of a physician's position in the network (e.g., by whether or not they are involved in cliques - groups of actors that are fully connected to each other - such as closed triangles in the case of three actors), this would further strengthen the case for targeting of select physicians for interventions. Using accompanying Medicare Part D data, we converted patient longitudinal prescription receipts into novel measures of the intensity of each physician's risky-prescribing. Exponential random graph models were used to simultaneously estimate the importance of homophily in prescribing and deprescribing in the network beyond the characteristics of physician specialty (or other metadata) and network-derived features. In addition, novel network measures were introduced to allow homophily to be characterized in relation to specific triadic (three-actor) structural configurations in the network with associated non-parametric randomization tests to evaluate their statistical significance in the network against the null hypothesis of no such phenomena. We found physician homophily in prescribing and deprescribing in both the state-wide and multiple HRR sub-networks, and that the level of homophily varied across HRRs. We also found that physicians exhibited within-triad homophily in risky-prescribing, with the prevalence of homophilic triads significantly higher than expected by chance absent homophily. These results may explain why communities of prescribers emerge and evolve, helping to justify group-level prescriber interventions. The methodology could be applied to arbitrary shared-patient networks and even more generally to other kinds of network data that underlies other kinds of social phenomena.