We examined the genetic architecture of functional brain connectivity measures in resting state electroencephalographic (EEG) recordings. Previous studies in Dutch twins have suggested that genetic factors are a main source of variance in functional brain connectivity derived from EEG recordings. In addition, qualitative descriptors of the brain network derived from graph analysis - network clustering and average path length - are also heritable traits. Here we replicated previous findings for connectivity, quantified by the synchronization likelihood, and the graph theoretical parameters cluster coefficient and path length in an Australian sample of 16-year-old twins (879) and their siblings (93). Modeling of monozygotic and dizygotic twins and sibling resemblance indicated heritability estimates of the synchronization likelihood (27-74%) and cluster coefficient and path length in the alpha and theta band (40-44% and 23-40% respectively) and path length in the beta band frequency (41%). This corroborates synchronization likelihood and its graph theoretical derivatives cluster coefficient and path length as potential endophenotypes for behavioral traits and neurological disorders.