To identify the core-periphery organization of the protein contact network it is subjected to core decomposition. The k-core of a network is defined as a subnetwork which exclusively contains nodes which connect to at least k other nodes in the same subnetwork (Seidman, 1983). The cores of different orders of a network can be obtained by iteratively removing all nodes which have less than k connections with other residues (k = 1, 2, …). This is done by first identifying all nodes whose degree (i.e., number of connections) is less than k. After removing these, the network is re-analyzed to determine if the removal of these nodes has resulted in other nodes (which originally had degree > k) having now less than k connections. If such nodes are identified, then they are removed, and the process is continued, until nomore nodes can be removed. The resulting subnetwork is called the k-core of the network.

Generation of k-core decomposition from 3-dimensional protein structure

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