# h-Centrality

#### Definition

The h-degree of a node is a basic indicator for weighted networks. In a weighted network with $N$ nodes, the h-centrality, $C_h$ of node $n$ is defined as:

$$C_h(n)= {d_h(n)\over N-1}$$

where $N$ denotes the total number of nodes in a network, $d_h(n)$ is the h-degree of node n. h-Centrality is just a normalized form of the h-degree.The h-degree $(d_h)$ of node n in a weighted network is equal to $d_h(n)$ if $d_h(n)$ is the largest natural number such that $n$ has at least $d_h(n)$ links each with strength at least equal to $d_h(n)$.

This approach is more suitable for weighted networks. It considers the number of links and the strength of links, and reflect more information about the links’ strength and structure.

$$C_h(n)= {d_h(n)\over N-1}$$

where $N$ denotes the total number of nodes in a network, $d_h(n)$ is the h-degree of node n. h-Centrality is just a normalized form of the h-degree.The h-degree $(d_h)$ of node n in a weighted network is equal to $d_h(n)$ if $d_h(n)$ is the largest natural number such that $n$ has at least $d_h(n)$ links each with strength at least equal to $d_h(n)$.

This approach is more suitable for weighted networks. It considers the number of links and the strength of links, and reflect more information about the links’ strength and structure.

#### References

- Zhao S., Rousseau R., Ye F., 2011. H-Degree as a basic measure in weighted networks. Journal of Informetrics, 5(4), pp.668-677. DOI: 10.1016/j.joi.2011.06.005