# WVoteRank

#### Definition

The $WVoteRank$ is a centrality method for identification of multiple spreaders on weighted complex networks.It is a novel approach $WVoteRank$ to find multiple spreaders by extending $VoteRank$. $VoteRank$ has limitations to select multiple spreaders on unweighted networks while various real networks are weighted networks . Thus $WVoteRank$ is generalized to deal with both unweighted and weighted networks by considering both degree and weight in voting process.

This method generalizes $VoteRank$ from unweighted networks to both unweighted and weighted networks as $WVoteRank$. In this method all nodes vote for a spreader using edge weight and neighbour number in each turn, and the voting ability of neighbours of selected spreader will be decreased in subsequent turns.

$$s_v={\sqrt{|\gamma (v)|{\underset {i\in \gamma (v)}{\sum} va_i * w_{(v,i)}}}} $$

To calculate the voting score $s_v$ of node $v$ on a weighted network. Given a node $v$ and its neighboring set $(v)$, the voting score $s_v$ of node $v$ is determined by three factors, the number of neighbors $|\gamma (v)|$, the voting score $va_i$ of each neighbor $i$ and the edge weight $w_{(v,i)}$ between node $v$ and node $i$. $s_v$ can be calculated as the square root of the product of two parts, the number of neighbors $|\gamma (v)|$ and weighted sum of $va_i$ of each neighbor $i$.

$VoteRank$ has limitations to assign spreaders only on unweighted networks. Thus the extended $VoteRank$ as $WVoteRank$ deals with both weighted and unweighted networks. Both node degree and edge weights are considered in this new method in voting process.

This method generalizes $VoteRank$ from unweighted networks to both unweighted and weighted networks as $WVoteRank$. In this method all nodes vote for a spreader using edge weight and neighbour number in each turn, and the voting ability of neighbours of selected spreader will be decreased in subsequent turns.

$$s_v={\sqrt{|\gamma (v)|{\underset {i\in \gamma (v)}{\sum} va_i * w_{(v,i)}}}} $$

To calculate the voting score $s_v$ of node $v$ on a weighted network. Given a node $v$ and its neighboring set $(v)$, the voting score $s_v$ of node $v$ is determined by three factors, the number of neighbors $|\gamma (v)|$, the voting score $va_i$ of each neighbor $i$ and the edge weight $w_{(v,i)}$ between node $v$ and node $i$. $s_v$ can be calculated as the square root of the product of two parts, the number of neighbors $|\gamma (v)|$ and weighted sum of $va_i$ of each neighbor $i$.

$VoteRank$ has limitations to assign spreaders only on unweighted networks. Thus the extended $VoteRank$ as $WVoteRank$ deals with both weighted and unweighted networks. Both node degree and edge weights are considered in this new method in voting process.

#### References

- Sun H.l., Chen D.b., He J.l., Ch\'ng E., 2019. A voting approach to uncover multiple influential spreaders on weighted networks. Physica A: Statistical Mechanics and its Applications, 519, pp.303-312. DOI: 10.1016/j.physa.2018.12.001