Core Discussion Network (CDN) includes relatively small number of people who provide or require social support and to whom a person feels emotionally close. These ties are also usually more durable than the ‘weak ties’ or acquaintanceship ties. The conventional way of studying CDNs is by means of ego-centric surveys – probability samples and administration of questionnaires involving a name generator interrogating respondents about people with whom they ‘discuss important matters’. Recent developments in Exponential-family Random Graph Models (ERGM) provide methods to use such egocentric data to model the existence of CDN ties by means of selected structural effects identical to those used in ERGMs fitted to complete networks (Krivitsky&Morris 2017; Krivitsky, Morris & Bojanowski 2021). Existing applications demonstrate that such models can include effects of nodal attributes, homophily effects, degree effects and triadic effects (provided that the data includes information on alter-alter ties). However, what has not been demonstrated thus far is that such an approach extends from the effects of dyadic covariates that are functions of node attributes (e.g. homophily effects) to effects of dyadic covariates that are not such functions (e.g. marriage ties). We illustrate the proposed approach using data from General Social Survey, discuss data requirements, advantages and limitations.