Local clustering coefficient-based iterative peeling strategy to extract the core and peripheral layers of a network

We propose a novel local clustering coefficient (LCC)-based strategy to extract the peripheral layers of a complex network and identify the nodes that be part of one of these layers as well as those that would form the core of the network. The LCC of a node is the probability that any two neighbors of the node are connected. Our hypothesis is that for any given network topology, nodes with a LCC of 1.0 ideally suit to the role of peripheral nodes. We propose an iterative peeling strategy wherein we remove the nodes with a LCC of 1.0 (the LCC values of the residual nodes are recalculated after each iteration) to extract the peripheral nodes at a particular layer (starting from the outermost peripheral layer to the innermost peripheral layer) and penetrate towards the inner core. We stop the iterative peeling when all the residual nodes (left over nodes in the network after the removal of the nodes at the peripheral layers) have a degree of 0 or the LCC values of all the non-zero degree residual nodes are less than 1.0. We show that the proposed LCC-based iterative peeling strategy has the potential to envision an inner most single-layer core and a hierarchical (one or more peripheral layers) peripheral structure for scale-free networks and a single layer of peer nodes (all nodes have a LCC of less than 1.0) for random networks.