All-pairs Shortest Dynamic Path Length Algorithm

Algorithm computing the shortest-dynamic-path-length between all pairs of nodes in a dynamic network

This function computes the Shortest Dynamic Path Length defined in the paper "Understanding and Modeling the Small-World Phenomenon in Dynamic Networks - AD. Nguyen et al - MSWIM 2012" between all pairs of nodes in a dynamic network.

Inputs:
- states: the temporal graphs under form of 3D-matrix in which the 1st and 2nd denotes node's IDs and the 3rd dimension denotes the time. states(:,:,t) is the network adjacency matrix at time t (i.e. state(i,j,t) = 1 if i is connected to j at time t and 0 otherwise). state(i,i,t) = 1 for all i. The shortest path lengths are calculated from the beginning of states.
- find_path: find the shortest paths if a non zero value was entered.

Outputs:
- d: the average shortest dynamic path length of the network.
- D: the matrix containing the shortest dynamic path lengths between all pairs of nodes.
- E: the list of encounters, if find_path is not equal to 0. The function findAllPaths uses this to find all the shortest paths between all pairs of nodes.

Please refer to the paper for more details.