Organization in complex brain networks: Energy distributions and phase shift

•In this work we focused on the understanding of variabilities in brain networks due to distribution of energy within the framework of constant Potts model.•The energy distribution calculated as a function of levels of organization is found to follow fractal behavior and is controlled by resolution parameter.•We also observe three different phases driven by this parameter which may correspond to different brain states and it may play a key role in regulating brain functions.•The fundamental basis of energy distributions in brain could reflect in the complicated brain dynamics. [Display omitted] The Hamiltonian function of a network, derived from the intrinsic distributions of nodes and edges, magnified by resolution parameter has information on the distribution of energy in the network. In brain networks, the Hamiltonian function follows hierarchical features reflecting a power-law behavior which can be a signature of self-organization. Further, the transition of three distinct phases driven by resolution parameter is observed which could correspond to various important brain states. This resolution parameter could thus reflect a key parameter that controls and balances the energy distribution in the brain network.