brainconn.distance.findpaths

findpaths(CIJ, qmax, sources, savepths=False)

Paths are sequences of linked nodes, that never visit a single node more than once. This function finds all paths that start at a set of source nodes, up to a specified length. Warning: very memory-intensive.

Parameters:

• CIJ (NxN numpy.ndarray) – binary directed/undirected connection matrix
• qmax (int) – maximal path length
• sources (Nx1 numpy.ndarray) – source units from which paths are grown
• savepths (bool) – True if all paths are to be collected and returned. This functionality is currently not enabled.

Returns:

• Pq (NxNxQ numpy.ndarray) – Path matrix with P[i,j,jq] = number of paths from i to j with length q
• tpath (int) – total number of paths found
• plq (Qx1 numpy.ndarray) – path length distribution as a function of q
• qstop (int) – path length at which findpaths is stopped
• allpths (None) – a matrix containing all paths up to qmax. This function is extremely complicated and reimplementing it in bctpy is not straightforward.
• util (NxQ numpy.ndarray) – node use index

Notes

Note that Pq(:,:,N) can only carry entries on the diagonal, as all “legal” paths of length N-1 must terminate. Cycles of length N are possible, with all vertices visited exactly once (except for source and target). ‘qmax = N’ can wreak havoc (due to memory problems).

Note: Weights are discarded. Note: I am certain that this algorithm is rather inefficient - suggestions for improvements are welcome.