EDCC - Effective Distance Closeness Centrality


Definition

EDCC consider not only the global structure of the network but also the local information of nodes. Closeness centrality EDCC of node $i$, denoted as $C_i^{eff}$

$$C_i^{eff}= {\left[{\underset{j}{\overset{N}{\sum}}}\right]}^{-1} D_{ji}$$

where $D_{ji}$ denotes the effective distance from node $i$ to node $j$. $D_{ji}$ is defined from an arbitrary reference node $i$ to another node $j$ in the network by the length of the shortest path from $i$ to $j$.

$$D_{ji}= {\underset{\Gamma}{\min}} \lambda(\Gamma)$$


$\lambda(\gamma)$ is the directed length of an ordered path $\gamma=\{i_1,...,i_L\}$ is defined, as the sum of effective lengths along the legs of the path

Compared with the classical $CC$, the main difference of $EDCC$ is that using effective distance to replace the conventional geographic distance or binary distance. Effective distance is obtained by the node’s input flow (in-degree in unweighted networks) and its neighbor’s output flow (outdegree in unweighted networks), and the EDCC carries more information about its neighbors than other centrality measures.



Comments

There are no comment yet.

Add your comment

Name:
Email:
Sum of    and  

The rendering mode: