The greedy procedure of k-core decomposition. The k-core decomposition procedure is illustrated with the toy example (from top to bottom, k = 1, 2, 3). Note that nodes with high degrees do not always reside in a k-shell with large k (see the comparison of nodes A, F, E and I for that matter in the legend box). Taking nodes F and G for example (in red), despite the fact they have the highest degree of connectivity (4) and are directly connected to the core nodes (A-D in yellow), they have the lowest k value (1). This indicates that via k-core decomposition, F and G are rated as peripheral hub nodes that have low contribution to the global integrity of the network.
Xie et al. BMC Evolutionary Biology 2011 11:242 doi:10.1186/1471-2148-11-242