Count n-length paths through a graph by matrix multiplication

README.md

Counting paths through a graph

You can count the number of n-long paths in a graph by taking the adjacency matrix for the graph and exponentiating it by n.

example.dot

digraph {
1 -> 1;
1 -> 2;
1 -> 3;
1 -> 4;
2 -> 3;
3 -> 4;
4 -> 4;
}

LICENSE

Copyright Thomas Sutton (c) 2015

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above
      copyright notice, this list of conditions and the following
      disclaimer in the documentation and/or other materials provided
      with the distribution.

    * Neither the name of Thomas Sutton nor the names of other
      contributors may be used to endorse or promote products derived
      from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Main.hs

{-# LANGUAGE TupleSections #-}
module Main where

import System.Environment
import Data.Graph
import Data.GraphViz
import Data.Text (Text)
import qualified Data.Text.Lazy as T
import qualified Data.Text.IO as T
import Sparse.Matrix

main :: IO ()
main = do
  [ k , f ] <- getArgs
  let n = read k :: Int
  g <- (parseDotGraphLiberally . T.fromStrict) <$> T.readFile f
  paths n g

paths :: Int -> DotGraph Int -> IO ()
paths k g = do
    let m = adjacency g
    print m
    print (m ^ k)

adjacency :: DotGraph Int -> Mat Word
adjacency g =
    let es = graphEdges g
        diag = adj $ map (\e -> Key (from e) (to e)) es
        bot = adj $ map (\e -> Key (to e) (from e)) $ filter (\e -> from e /= to e) es
    in diag + bot
  where
    from = fromIntegral . fromNode
    to = fromIntegral . toNode
    adj = fromList . map (,1)

paths.cabal

name:                paths
version:             0.1.0.0
synopsis:            Count paths in a graph.
description:         Please see README.md
homepage:            https://gist.github.com/thsutton/3f67d5b65c06f3ace318
license:             BSD3
license-file:        LICENSE
author:              Thomas Sutton
maintainer:          [email protected]
copyright:           2015 Thomas Sutton
category:            Graphs
build-type:          Simple
cabal-version:       >=1.10

executable paths
  main-is:             Main.hs
  default-language:    Haskell2010
  build-depends:       base >= 4.7 && < 5
                     , containers
                     , graphviz
                     , sparse
                     , text

Setup.hs

import Distribution.Simple
main = defaultMain

stack.yaml

resolver: lts-3.4
packages:
- '.'
extra-deps:
- sparse-0.9.2
- hybrid-vectors-0.2
- graphviz-2999.18.0.1
flags: {}