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Identifying Influential Nodes in Weighted Networks using k-shell based HookeRank Algorithm

Finding influential spreaders is a crucial task in the field of network analysis because of numerous theoretical and practical importance. These nodes play vital roles in the information diffusion process, like viral marketing. Many real-life networks are weighted networks, but relatively less work has been done for finding influential nodes in the case of weighted networks as compared to unweighted networks. In this paper, we propose a k-shell-based HookeRank (KSHR) algorithm to identify spreaders in weighted networks. First, we propose weighted k-shell centrality of the node u by using the k-shell value of $u$, the k-shell value of its neighbors ($v$), and edge weight ($w_{uv}$) between them. We model edges present in the network as springs and edge weights as spring constants. Based on the notion of Hooke's law of elasticity, we assume a force equal to the weighted k-shell value acts on each node. In this arrangement, we formulate the KSHR centrality of each node using associated weighted k-shell value and the equivalent edge weight by taking care of series and parallel combination of edges up to 3-hop neighbors from the source node. The proposed algorithm finds influential nodes that can spread the information to the maximum number of nodes in the network. We compare our proposed algorithm with popular existing algorithms and observe that it outperforms them on many real-life and synthetic networks suing Susceptible-Infected-Recovered (SIR) information diffusion model.