# Mobility Centrality

#### Definition

This method is constructed by the use of the anagogic method considering the formula of the kinetic energy of a particle in Physics and adjusting its mathematical analogue to the case of the interregional road network. This centrality represents by $C_i^m$ and defines as fallows:

$$C_i^m={w_i\over 2(N-1)}. {\underset{j=1,i\ne j}{\overset{N}{\sum}}} , \left({d_{ij}^E} \over {w_{ji}}\right)$$

were $w_i$ is node’s weight and $d_{ij}$ is the network distance, $N$ expresses the dimension of the set $V (N = |V |)$ for the network $G(V,E)$ and impedance weight that represented by $w_{ji}$ of the edge $E$.

This centrality measure is estimated to be useful for the operational analysis of a network (such as the analysis of network flows), since it characterizes as central these vertices that appear to have the greatest tendency to attract or expel network flows.

$$C_i^m={w_i\over 2(N-1)}. {\underset{j=1,i\ne j}{\overset{N}{\sum}}} , \left({d_{ij}^E} \over {w_{ji}}\right)$$

were $w_i$ is node’s weight and $d_{ij}$ is the network distance, $N$ expresses the dimension of the set $V (N = |V |)$ for the network $G(V,E)$ and impedance weight that represented by $w_{ji}$ of the edge $E$.

This centrality measure is estimated to be useful for the operational analysis of a network (such as the analysis of network flows), since it characterizes as central these vertices that appear to have the greatest tendency to attract or expel network flows.