  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.
