Figure 1
From: K-core robustness in ecological and financial networks
K-shell decomposition of an example network. The network shown here has undergone the k-shell decomposition described above. At each step of the algorithm, nodes with degree equal to or less than k are removed iteratively until none remain. These nodes are then said to belong to the k-th shell. The innermost shell kmax, or the core of the network, contains the nodes with the highest degree even after the iterative pruning, which are the ones responsible for providing a “structure” to the network with their high interaction strengths. Those in the outermost shell (or shells, in larger networks) are vital for network survival under random attack, where a greater number of “expendable” nodes in the outer shells decreases the chances of a vital node being removed. The “U”-shaped k-shell occupancy levels described in this paper therefore lead to networks that are more robust under both global and local attacks.
