# Weighted H-index Centrality

#### Definition

This method proposes a weight edge by the product of two degrees of connected nodes. And then utilize the operator $H$ on the neighbors of each node which are extended by $k$ weight edges, where $k$ is the degree of each neighbor. The sum of neighbors’ weighted $h$-index values defines the importance of a node.Calculating the weight $h$-index centrality has a complexity of $O(m)$ were $m$ is the number of edges.
The weighted $h$-index centrality is more efficient than other time-consuming measure such as betweenness centrality and closeness centrality.

The h-index centrality $(WH)$ of node $i$ is define as follow:

$$WH(i)={\sum}_{v_j\in \Gamma (i)}wh_j$$

were $wh_j$ is weighted h-index of node $j$.

#### References

• Gao L., Yu S., Li M., Shen Z., Gao Z., 2019. Weighted h-index for identifying influential spreaders. Symmetry, 11(10). DOI: 10.3390/sym11101263