# LCCDC - Local Clustering Coefficient-based Degree Centrality

#### Definition

The hypothesis behind this method is that nodes with a high degree, but low local clustering coefficient, are more likely to be on the shortest paths of several node pairs and are likely to incur a larger BWC value. Accordingly, we define the local clustering coefficient-based degree centrality (LCCDC) for a node as the product of the degree centrality of the node and one minus the local clustering coefficient of the node. LCCDC defines as follows;

$$LCCDC_{(v_i)}=k_i*(1-LCC{(v_i)})$$

were $LCC$ is the local clustering coefficient of a vertex that defines by the ratio of the actual number of links between the neighbors of the vertex to that of the maximum possible number of links between the neighbors of the vertex, $k_i$ is the number of neighbor node of vortex $v_i$. The LCCDC of a node can be computed based on just the knowledge of the two-hop neighborhood of a node and would take significantly lower time.

$$LCCDC_{(v_i)}=k_i*(1-LCC{(v_i)})$$

were $LCC$ is the local clustering coefficient of a vertex that defines by the ratio of the actual number of links between the neighbors of the vertex to that of the maximum possible number of links between the neighbors of the vertex, $k_i$ is the number of neighbor node of vortex $v_i$. The LCCDC of a node can be computed based on just the knowledge of the two-hop neighborhood of a node and would take significantly lower time.

#### References

- Meghanathan, N., 2017. A computationally lightweight and localized centrality metric in lieu of betweenness centrality for complex network analysis. Vietnam Journal of Computer Science, 4(1), pp.23-38. DOI: 10.1007/s40595-016-0073-1