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