A k-shell decomposition method for weighted networks

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptible-infectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.

💡 Research Summary

The paper introduces a generalized k‑shell (or k‑core) decomposition method that explicitly incorporates edge weights, thereby extending the classic degree‑only approach to weighted networks. The authors define a composite node strength (s_i = k_i^\alpha w_i^{1-\alpha}), where (k_i) is the ordinary degree, (w_i = \sum_j w_{ij}) is the weighted degree (the sum of incident edge weights), and (\alpha\in