# algorithm - undirected - total number of paths in a graph

## Algorithm to find the number of distinct paths in a directed graph (1)

If you follow a slightly modified Dijkstra's algorithm, you can have an all-pair solution.

Explanation: Paths from `u` to `v` is the sum of the following:

1. Paths from `u` to `v` which doesn't pass through `w`
2. Paths which go through `w` = number of paths from `u` to `w` times number of paths from `w` to `v`

Initialise the matrix with zeros except when there is an edge from `i` to `j` (which is 1). Then the following algorithm will give you the result (all-pair-path-count)

``````for i = 1 to n:
for j = 1 to n:
for k = 1 to n:
paths[i][i] += paths[i][k] * paths[k][j]
``````

Needless to say : `O(n^3)`

Eager to read a single pair solution. :)

Possible Duplicate:
Graph Algorithm To Find All Connections Between Two Arbitrary Vertices

I have a directed graph, what algorithm can i use to find the number of distinct acyclic paths between 2 particular vertices, and count the maximum times any path is used in these distinct paths? Two paths are distinct if they either visit a different number of vertices or visit vertices in a different order.