Network Distance Statistics

Distance between nodes is the shortest Path between them.

Can be used to measure node importance or analyze the structure of a Graph.

• Eccentricity
• Radius of a Graph
• Diameter of a Graph

These measures can be used to discriminate among different networks:

Average Length of Shortest Paths: $\bar{d}(u)=\frac{1}{|V|-1}{\sum }_{v\in V(G),v\ne u}d(u,v)$ Average Path Length: $\bar{d}(G)=\frac{1}{|V|}{\sum }_{u\in V}\bar{d}(u)$ Characteristic Path Length (Median): $\mathrm{median}\{\bar{d}(u)\mid u\in V(G)\}$