Graph algorithms in lua
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README.md

lua-graph

Graph algorithms in lua

Features

The graph algorithms covered:

  • Graph data structure (directed / undirected / weighted / unweighted)
  • Depth first search
  • Breadth first search
  • Connected components
  • Strongly connected components
  • Topological sort
  • Minimum spanning tree (Kruskal)
  • Minimum spanning tree (Prim)
  • Max flow min cut
  • Dijkstra shortest paths
  • Topogical sort shortest paths
  • Bellman Ford shortest paths

Notes

For developers who have been using library 1.0.2, the main changes are:

  • graph.V is removed and replaced with graph:vertexCount() and graph:vertexAt(index) method for iterating all vertices: this change was introduced so that graph vertices do not need to start with vertex 0 and do not need to be consecutive integer (can be any label).
  • graph:addVertexIfNotExists: allows user to add vertices later after the graph is created
  • graph:removeVertex: allows user to delete a vertex and its edges
  • graph:addEdge: Now if the vertices on which the edge is to be added does not exists in the graph, they will be automatically added

Install

luarocks install luagraphs

Usage

Create an undirected unweighted graph

local g = require('luagraphs.data.graph').create(6)
g:addEdge(0, 5) -- bidirectional edge connecting 0 and 5
g:addEdge(2, 4)
g:addEdge(2, 3)
g:addEdge(1, 2)
g:addEdge(0, 1)
g:addEdge(3, 4)
g:addEdge(3, 5)
g:addEdge(0, 2)

print(g:vertexCount()) -- return 6

-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all the vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        text = text .. ', ' .. adj_v:get(i):other(v)
    end
    print(text)
end

Create an undirected unweighted graph and add / remove vertices later

local g = require('luagraphs.data.graph').create(6)
g:addEdge(0, 5) -- bidirectional edge connecting 0 and 5
g:addEdge(2, 4)
g:addEdge(2, 3)
g:addEdge(1, 2)
g:addEdge(0, 1)
g:addEdge(3, 4)
g:addEdge(3, 5)
g:addEdge(0, 2)

-- expand the graph by another 3 vertices: -1, 9, and 10
-- if you want to add a vertex without adding an edge, can just call g:addVertexIfNotExists(vertexId) instead
g:addEdge(-1, 10) 
g:addEdge(9, 2)
g:addEdge(-1, 0)

print(g:containsVertex(9)) -- return true
print(g:containsVertex(-1)) -- return true
print(g:containsVertex(8)) -- return false

print(g:vertexCount()) -- return 9

-- to remove a vertex, can just call g:removeVertex(vertexId)

-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all the vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        text = text .. ', ' .. adj_v:get(i):other(v)
    end
    print(text)
end

Create an undirected unweighted graph from a list of vertices and expand or shrink it

local vertices = require('luagraphs.data.list').create()
vertices:add(3)
vertices:add(5)
vertices:add(10)

local g = require('luagraphs.data.graph').createFromVertexList(vertices)

print(g:vertexCount()) -- return 3

g:addVertexIfNotExists(4)
g:addVertexIfNotExists(5)

print(g:vertexCount()) -- return 4

g:addEdge(0, 5) -- add a new vertex 0 and a bidirectional edge connecting 0 and 5

print(g:vertexCount()) -- return 5

g:removeVertex(10)

print(g:vertexCount()) -- return 4


-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all the vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        text = text .. ', ' .. adj_v:get(i):other(v)
    end
    print(text)
end

Create an directed unweighted graph

local g = require('luagraphs.data.graph').create(6, true) -- true means it is directed
g:addEdge(0, 5) -- edge directed from 0 to 5
g:addEdge(2, 4)
g:addEdge(2, 3)
g:addEdge(1, 2)
g:addEdge(0, 1)
g:addEdge(3, 4)
g:addEdge(3, 5)
g:addEdge(0, 2)

print(g:vertexCount()) -- return 6

-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        local e = adj_v:get(i)
        text = text .. ', ' .. e:other(v)
    end
    print(text)
end

Create an undirected weighted graph

local g = require('luagraphs.data.graph').create(6)
g:addEdge(0, 5, 1.2) -- bidirectional edge with weight equal to 1.2 and connecting between 0 and 5
g:addEdge(2, 4, 2.2)
g:addEdge(2, 3, 1.2)
g:addEdge(1, 2, 1.2)
g:addEdge(0, 1, 2.2)
g:addEdge(3, 4, 1.2)
g:addEdge(3, 5, 2.2)
g:addEdge(0, 2, 2.2)

print(g:vertexCount()) -- return 6

-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        local e = adj_v:get(i)
        text = text .. ', ' .. e:other(v) .. '(' .. e.weight .. ')' 
    end
    print(text)
end

Create an directed weighted graph

local g = require('luagraphs.data.graph').create(6, true) -- true means directed
g:addEdge(0, 5, 1.2) -- bidirectional edge with weight equal to 1.2 and connecting between 0 and 5
g:addEdge(2, 4, 2.2)
g:addEdge(2, 3, 1.2)
g:addEdge(1, 2, 1.2)
g:addEdge(0, 1, 2.2)
g:addEdge(3, 4, 1.2)
g:addEdge(3, 5, 2.2)
g:addEdge(0, 2, 2.2)

print(g:vertexCount()) -- return 6

-- code below prints the adjacency list 
for k = 0, g:vertexCount() -1 do -- iterate through all vertices in g
    local v = g:vertexAt(k)
    local adj_v = g:adj(v) -- adjacency list for vertex v
    local text = ''
    for i = 0, adj_v:size()-1 do
        local e = adj_v:get(i)
        text = text .. ', ' .. e:other(v) .. '(' .. e.weight .. ')' 
    end
    print(text)
end

Depth First Search

local g = require('luagraphs.data.graph').create(6)
g:addEdge(0, 5)
g:addEdge(2, 4)
g:addEdge(2, 3)
g:addEdge(1, 2)
g:addEdge(0, 1)
g:addEdge(3, 4)
g:addEdge(3, 5)
g:addEdge(0, 2)
local dfs = require('luagraphs.search.DepthFirstSearch').create()
local s = 0
dfs:run(g, s)

for k = 0, g:vertexCount()-1 do
    local v = g:vertexAt(k)
    if v ~= s and dfs:hasPathTo(v) then
        print('has path to ' .. v)
        local path = dfs:getPathTo(v)
        local pathText = ''
        while path:isEmpty() == false do
            local x = path:pop()
            if pathText == '' then
                pathText = pathText .. x
            else
                pathText = pathText .. ' -> ' .. x
            end
        end
        print(pathText)

    end
end

Breadth First Search

local g = require('luagraphs.data.graph').create(6) 
g:addEdge(0, 5)
g:addEdge(2, 4)
g:addEdge(2, 3)
g:addEdge(1, 2)
g:addEdge(0, 1)
g:addEdge(3, 4)
g:addEdge(3, 5)
g:addEdge(0, 2)
local bfs = require('luagraphs.search.BreadthFirstSearch').create()
local s = 0
bfs:run(g, s)

for k = 0, g:vertexCount()-1 do
    local v = g:vertexAt(k)
    if v ~= s and bfs:hasPathTo(v) then
        local path = bfs:getPathTo(v)
        local pathText = ''
        while path:isEmpty() == false do
            local x = path:pop()
            if pathText == '' then
                pathText = pathText .. x
            else
                pathText = pathText .. ' -> ' .. x
            end
        end
        print(pathText)

    end
end

Connected Components

local g = require('luagraphs.data.graph').create(13) -- undirected graph
g:addEdge(0, 5)
g:addEdge(4, 3)
g:addEdge(0, 1)
g:addEdge(9, 12)
g:addEdge(6, 4)
g:addEdge(5, 4)
g:addEdge(0, 2)
g:addEdge(11, 12)
g:addEdge(9,10)
g:addEdge(0, 6)
g:addEdge(7, 8)
g:addEdge(9, 11)
g:addEdge(5, 3)

local cc = require('luagraphs.connectivity.ConnectedComponents').create()
cc:run(g)

print('count: ' .. cc.count)
print(cc.count) -- return 3 connected components
for k = 0,g:vertexCount()-1 do
    local v = g:vertexAt(k)
    print('id[' .. v .. ']: ' .. cc:component(v))
end

Strongly Connected Components

local graph = require('luagraphs.data.graph').create(13, true) -- directed graph
graph:addEdge(4, 2)
graph:addEdge(2, 3)
graph:addEdge(3, 2)
graph:addEdge(6, 0)
graph:addEdge(0, 1)
graph:addEdge(2, 0)
graph:addEdge(11, 12)
graph:addEdge(12, 9)
graph:addEdge(9, 10)
graph:addEdge(9, 11)
graph:addEdge(8, 9)
graph:addEdge(10, 12)
graph:addEdge(11, 4)
graph:addEdge(4, 3)
graph:addEdge(3, 5)
graph:addEdge(7, 8)
graph:addEdge(8, 7)
graph:addEdge(5, 4)
graph:addEdge(0, 5)
graph:addEdge(6, 4)
graph:addEdge(6, 9)
graph:addEdge(7, 6)

local scc = require('luagraphs.connectivity.StronglyConnectedComponents').create()
scc:run(graph)
print(scc.count) -- return 5 components

for k = 0,graph:vertexCount()-1 do
    local v = graph:vertexAt(k)
    print('id[' .. v .. ']: ' .. scc:component(v))
end

Topological Sort

local dag = require('luagraphs.data.graph').create(7, true) -- directed acyclic graph

dag:addEdge(0, 5)
dag:addEdge(0, 2)
dag:addEdge(0, 1)
dag:addEdge(3, 6)
dag:addEdge(3, 5)
dag:addEdge(3, 4)
dag:addEdge(5, 4)
dag:addEdge(6, 4)
dag:addEdge(6, 0)
dag:addEdge(3, 2)
dag:addEdge(1, 4)

local ts = require('luagraphs.sort.TopologicalSort').create()
ts:run(dag)

local path = ts:path()
for i=0, path:size()-1 do
    print('sort #' .. i .. ': ' .. path:get(i))
end

Minimum Spanning Tree (Kruskal)

local mst = require('luagraphs.mst.KruskalMST').create() 
local g = require('luagraphs.data.graph').create(8) -- undirected graph with weighted edges
g:addEdge(0, 7, 0.16) -- 0.16 is the weight of the edge between 0 and 7
g:addEdge(2, 3, 0.17)
g:addEdge(1, 7, 0.19)
g:addEdge(0, 2, 0.26)
g:addEdge(5, 7, 0.28)
g:addEdge(1, 3, 0.29)
g:addEdge(1, 5, 0.32)
g:addEdge(2, 7, 0.34)
g:addEdge(4, 5, 0.35)
g:addEdge(1, 2, 0.36)
g:addEdge(4, 7, 0.37)
g:addEdge(0, 4, 0.38)
g:addEdge(6, 2, 0.4)
g:addEdge(3, 6, 0.52)
g:addEdge(6, 0, 0.58)
g:addEdge(6, 4, 0.93)

mst:run(g)

local path = mst.path

print(path:size()) -- return 7
for i=0,path:size()-1 do
    local e = path:get(i)
    print(e:from() .. ' -> ' .. e:to() .. ' (' .. e.weight .. ')')
end

Minimum Spanning Tree (Prim)

local mst = require('luagraphs.mst.PrimMST').create()
local g = require('luagraphs.data.graph').create(8) -- undirected graph with weighted edges
g:addEdge(0, 7, 0.16) -- 0.16 is the weight of the edge between 0 and 7
g:addEdge(2, 3, 0.17)
g:addEdge(1, 7, 0.19)
g:addEdge(0, 2, 0.26)
g:addEdge(5, 7, 0.28)
g:addEdge(1, 3, 0.29)
g:addEdge(1, 5, 0.32)
g:addEdge(2, 7, 0.34)
g:addEdge(4, 5, 0.35)
g:addEdge(1, 2, 0.36)
g:addEdge(4, 7, 0.37)
g:addEdge(0, 4, 0.38)
g:addEdge(6, 2, 0.4)
g:addEdge(3, 6, 0.52)
g:addEdge(6, 0, 0.58)
g:addEdge(6, 4, 0.93)

mst:run(g)

local path = mst.path

print(path:size()) -- return 7
for i=0,path:size()-1 do
    local e = path:get(i)
    print(e:from() .. ' -> ' .. e:to() .. ' (' .. e.weight .. ')')
end

Minimum Spanning Tree (Eager Prim)

local mst = require('luagraphs.mst.EagerPrimMST').create()
local g = require('luagraphs.data.graph').create(8) -- undirected graph with weighted edges
g:addEdge(0, 7, 0.16) -- 0.16 is the weight of the edge between 0 and 7
g:addEdge(2, 3, 0.17)
g:addEdge(1, 7, 0.19)
g:addEdge(0, 2, 0.26)
g:addEdge(5, 7, 0.28)
g:addEdge(1, 3, 0.29)
g:addEdge(1, 5, 0.32)
g:addEdge(2, 7, 0.34)
g:addEdge(4, 5, 0.35)
g:addEdge(1, 2, 0.36)
g:addEdge(4, 7, 0.37)
g:addEdge(0, 4, 0.38)
g:addEdge(6, 2, 0.4)
g:addEdge(3, 6, 0.52)
g:addEdge(6, 0, 0.58)
g:addEdge(6, 4, 0.93)

mst:run(g)

local path = mst.path

print(path:size()) -- return 7
for i=0,path:size()-1 do
    local e = path:get(i)
    print(e:from() .. ' -> ' .. e:to() .. ' (' .. e.weight .. ')')
end

Shortest Paths (Dijkstra)

local g = require('luagraphs.data.graph').create(8, true); -- directed weighted graph

g:addEdge(0, 1, 5.0) -- edge from 0 to 1 is 5.0 in distance
g:addEdge(0, 4, 9.0)
g:addEdge(0, 7, 8.0)
g:addEdge(1, 2, 12.0)
g:addEdge(1, 3, 15.0)
g:addEdge(1, 7, 4.0)
g:addEdge(2, 3, 3.0)
g:addEdge(2, 6, 11.0)
g:addEdge(3, 6, 9.0)
g:addEdge(4, 5, 5.0)
g:addEdge(4, 6, 20.0)
g:addEdge(4, 7, 5.0)
g:addEdge(5, 2, 1.0)
g:addEdge(5, 6, 13.0)
g:addEdge(7, 5, 6.0)
g:addEdge(7, 2, 7.0)

local source = 0
local dijkstra = require('luagraphs.shortest_paths.Dijkstra').create()
dijkstra:run(g, source) -- 0 is the id of the source node in the path search
for k = 0,g:vertexCount()-1 do
    local v = g:vertexAt(k)
    if v ~= source and dijkstra:hasPathTo(v) then
        print('path from 0 to ' .. v .. ' ( cost: '  .. dijkstra:getPathLength(v) .. ' )')
        local path = dijkstra:getPathTo(v)
        for i = 0,path:size()-1 do
            print('# from ' .. path:get(i):from() .. ' to ' .. path:get(i):to() .. ' ( distance: ' .. path:get(i).weight .. ' )')
        end
    end
end

Shortest Paths (Topological Sort)

local g = require('luagraphs.data.graph').create(8, true); -- directed weighted graph

g:addEdge(0, 1, 5.0) -- edge from 0 to 1 is 5.0 in distance
g:addEdge(0, 4, 9.0)
g:addEdge(0, 7, 8.0)
g:addEdge(1, 2, 12.0)
g:addEdge(1, 3, 15.0)
g:addEdge(1, 7, 4.0)
g:addEdge(2, 3, 3.0)
g:addEdge(2, 6, 11.0)
g:addEdge(3, 6, 9.0)
g:addEdge(4, 5, 5.0)
g:addEdge(4, 6, 20.0)
g:addEdge(4, 7, 5.0)
g:addEdge(5, 2, 1.0)
g:addEdge(5, 6, 13.0)
g:addEdge(7, 5, 6.0)
g:addEdge(7, 2, 7.0)

local source = 0
local finder = require('luagraphs.shortest_paths.Dijkstra').create()
finder:run(g, source) -- 0 is the source node in the path search
for k = 0,g:vertexCount()-1 do
    local v= g:vertexAt(k)
    if v ~= source and finder:hasPathTo(v) then
        print('path from 0 to ' .. v .. ' ( cost: '  .. finder:getPathLength(v) .. ' )')
        local path = finder:getPathTo(v)
        for i = 0,path:size()-1 do
            print('# from ' .. path:get(i):from() .. ' to ' .. path:get(i):to() .. ' ( distance: ' .. path:get(i).weight .. ' )')
        end
    end
end

MinCut-MaxFlow (Ford Fulkerson implementation)

local g = require('luagraphs.data.network').FlowNetwork.create(8);

g:addEdge(0, 1, 10); -- capacity from vertex 0 to vertex 1 is 10
g:addEdge(0, 2, 5);
g:addEdge(0, 3, 15);
g:addEdge(1, 4, 9);
g:addEdge(1, 5, 15);
g:addEdge(1, 2, 4);
g:addEdge(2, 5, 8);
g:addEdge(2, 3, 4);
g:addEdge(3, 6, 16);
g:addEdge(4, 5, 15);
g:addEdge(4, 7, 10);
g:addEdge(5, 7, 10);
g:addEdge(5, 6, 15);
g:addEdge(6, 2, 6);
g:addEdge(6, 7, 10);

local method = require('luagraphs.flow.FordFulkerson').create()
local maxFlow = method:run(g, 0, 7)
print('FordFulkerson max flow: ' .. maxFlow)


local minCuts = method:minCuts()

for i = 0,minCuts:size()-1 do
    local e =minCuts:get(i)
    print('min cut: ' .. e:toString())
end