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.

These measures can be used to discriminate among different networks:

Average Length of Shortest Paths:

dˉ(u)=1∣V∣−1∑v∈V(G),v≠ud(u,v)\bar{d}(u)=\frac{1}{|V|-1} \sum_{v \in V(G), v \neq u} d(u, v)

Average Path Length:

dˉ(G)=1∣V∣∑u∈Vdˉ(u)\bar{d}(G)=\frac{1}{|V|} \sum_{u \in V} \bar{d}(u)

Characteristic Path Length (Median):

median⁡{dˉ(u)∣u∈V(G)}\operatorname{median}\{\bar{d}(u) \mid u \in V(G)\}