We present a statistical method of analysis of biological networks based on the exponential random graph model, namely p2-model, as opposed to previous descriptive approaches. The model is capable to capture generic and structural properties of a network as emergent from local interdependencies and uses a limited number of parameters. Here, we consider one global parameter capturing the density of edges in the network, and local parameters representing each nodes contribution to the formation of edges in the network. The modelling suggests a novel definition of important nodes in the network, namely social, as revealed based on the local sociality parameters of the model. Moreover, the sociality parameters help to reveal organizational principles of the network. An inherent advantage of our approach is the possibility of hypotheses testing: a priori knowledge about biological properties of the nodes can be incorporated into the statistical model to investigate its influence on the structure of the network.