This paper presents an application of Statistical Mechanics for analysis of critical phenomena in complex networks. Using the simulation model of a wired communication grid, the nature of phase transition is characterized and the corresponding critical exponent is computed. Network analogs of thermodynamic quantities such as order parameter, temperature, pressure, and composition are defined and the associated network phase diagrams are constructed. The notion of network eutectic point is introduced by showing characteristic similarities between the network phase diagram and the binary phase diagram. A concept of robust and resilient control in communication networks is presented based on network phase diagrams.