question: Genomic epidemiology is now widely used for viral outbreak investigations. Still, this methodology faces many challenges. First, few methods account for intra-host viral diversity. Second, maximum parsimony principle continues to be employed, even though maximum likelihood or Bayesian models are usually more consistent. Third, many methods utilize case-specific data, such as sampling times or infection exposure intervals. This impedes study of persistent infections in vulnerable groups, where such information has a limited use. Finally, most methods implicitly assume that transmission events are independent, while common source outbreaks violate this assumption. We propose a maximum likelihood framework SOPHIE (SOcial and PHilogenetic Investigation of Epidemics) based on integration of phylogenetic and random graph models. It infers transmission networks from viral phylogenies and expected properties of inter-host social networks modelled as random graphs with given expected degree distributions. SOPHIE is scalable, accounts for intra-host diversity and accurately infers transmissions without case-specific epidemiological data. SOPHIE code is freely available at https://github.com/compbel/SOPHIE/