# CHM - H-Index Mixing Centrality

#### Definition

The clustering H-index mixing $(CHM)$ centrality is based on the $H$-index of the node itself and the relative distance of its neighbors. Starting from the node itself and combining with the topology around the node, the importance of the node and its spreading capability were determined. The clustered $H$ index mixing $(CHM)$ method of node $v_i$ is calculated by the following relation:

$$CHM(v_i)=(1 + C_i) \left({\underset{j \in \varphi_i }{\sum}} {A_i\over d_{ij}^2}\right)$$

where $C_i$ represents the value of clustering coefficient of node $v_i$. In addition, $\varphi_i$ represents the set of neighboring nodes with the shortest path length less than the specified length (i.e., $d_{ij}\leq r$, without loss of generality, r set to 3 since the network size is so large that the computing cost is very high if r > 3), and node j is an element of $\varphi_i$.

The proposed method comprehensively considers the topological structure of nodes and the properties of their neighbors, and subdivides the spreading capability of each node according to the location of the neighbor nodes, so as to reflect the different importance of nodes more accurately.

$$CHM(v_i)=(1 + C_i) \left({\underset{j \in \varphi_i }{\sum}} {A_i\over d_{ij}^2}\right)$$

where $C_i$ represents the value of clustering coefficient of node $v_i$. In addition, $\varphi_i$ represents the set of neighboring nodes with the shortest path length less than the specified length (i.e., $d_{ij}\leq r$, without loss of generality, r set to 3 since the network size is so large that the computing cost is very high if r > 3), and node j is an element of $\varphi_i$.

The proposed method comprehensively considers the topological structure of nodes and the properties of their neighbors, and subdivides the spreading capability of each node according to the location of the neighbor nodes, so as to reflect the different importance of nodes more accurately.

#### References

- Lu P., Dong C., 2019. Ranking the spreading influence of nodes in complex networks based on mixing degree centrality and local structure. International Journal of Modern Physics B, 33(32). DOI: 10.1142/S0217979219503958