goraph is a pure Go library for graph data structure. This is rather a reference project. This contains complicated pointer examples and other data structure usage in Go. For graph APIs, I highly recommend Cayley.
Package goraph implements graph data structures and algorithms. It interacts with DOT and JSON format files.
To visualize, use the method ToDOTFile and open the dot file with Graphviz. Examples can be found here.
- Getting Started
- Package Hierarchy
- Sample Usage
- List(Linked List) vs. Slice(Array)
- What is Graph? (YouTube Clips)
- Adjacency List vs. Adjacency Matrix
- Channel
- C++ Version
- package gotree
go get github.com/gyuho/goraphgoraph uses the package gs as default, which discourage to have duplicate edges but still provides ways to implement it. Default formats are JSON and DOT as follows:
{
"testgraph": {
"S": {
"A": [100],
"B": [14],
"C": [200]
},
"A": {
"S": [15],
"B": [5],
"D": [20],
"T": [44]
}
}
}digraph testgraph {
S -> A [label=100]
S -> B [label=14]
S -> C [label=200]
}goraph
algorithm // Graph Algorithms
bfs // Breadth First Search (BFS)
dfs // Depth First Search (DFS)
maxflow // Maximum Flow
fdfk // Ford-Fulkerson's Maximum Network Flow
mst // Minimum Spanning Tree
kruskal // Kruskal's Minimum Spanning Tree
prim // Prim's Minimum Spanning Tree
scc // Strongly Connected Components
kosaraju // Kosaraju's Strongly Connected Components
tarjan // Tarjan's Strongly Connected Components
sp // Shortest Path
spbf // Shortest Path using Bellman-Ford algorithm
spd // Shortest Path using Dijkstra algorithm
spfw // Shortest Path using Floyd-Warshall algorithm
tsdag // Topological Sort
tsdfs // Topological Sort using DFS
tskahn // Topological Sort based on Arthur Kahn(1962)'s paper
goroup // Set Theory
gosequence // Sequence using slice
graph // Graph Data Structure
gl // Adjacency List, `container/list`
gm // Map Data Structure
gs // Slice, Sequence (Default in Goraph)
gt // Adjacency Matrix
helper // Helper function for graphs
gson // JSON Encoding, Decoding
parsex // Parser for JSON, DOT files
dotx // `dot` file parser
dotxd // allow duplicate edges
jsonx // `json` file parser
jsonxd // allow duplicate edges
usage // Example Scripts, ProgramsCode to calculate and visualize the shortest path from S to T:
package main
import (
"github.com/gyuho/goraph/algorithm/spd"
"github.com/gyuho/goraph/graph/gs"
)
func main() {
g4 := gs.FromJSON("../../../files/testgraph.json", "testgraph.004")
spd.VizDOTFile(g4, g4.FindVertexByID("S"), g4.FindVertexByID("T"), "test.dot")
}Output:
More examples can be found here.
Goraph mainly uses customized slice(array) data structure implemented in package gsd, instead of using linked list. To store vertices and edges, we can either use "container/list" or slice(array) data structure. It depends on the number of elements in the lists. Linked list will be more efficient, when we need to do many deletions in the 'middle' of the list. The more elements we have in graph , the less efficient a slice becomes. When the ordering of the elements isn't important, then it is most efficient to use a slice and deleting an element by replacing it by the last element and reslicing to shrink the size(len) by 1. We can mitigate the deletion problem using this slice trick but there is no way to mitigate the slowness of traversing linked list. Both ways are implemented, but mainly this will be run with slice.
Here's my benchmarks on "List(Linked List) vs. Slice(Array)", in which slice is x20,000 faster than linked list when traversing 5,0000 nodes.
Reference
- Go(Golang) Slice vs. List?
- Bjarne Stroustrup: Why you should avoid Linked Lists (C++)
- Why you should never use linked-list
-
Graph: Data Structure with Nodes and Edges
-
There are various ways to connect nodes
- Doubly Connected Directed Graph (Undirected Graph)
- Singly Connected Directed Graph.
-
Path: sequence of vertices connected by edges
-
Simple Path: path with NO repeated vertices
-
Cycle: path with at least one edge whose first and last vertices are the same
-
Simple Cycle: cycle with NO repeated edges or vertices
-
Length of path, cycle: its number of edges
-
Connectivity: Graph is connected if there is a path from every vertex to every other vertex
-
Acyclic Graph: graph with NO cycles
-
Acyclic Connected Graph: Tree is an Acyclic Connected Graph
-
Forest: Disjoint Set of Trees (have no vertices in common)
-
Spanning Tree of a Connected Graph
- subgraph that contains all of that graph’s vertices subgraph that is a single tree
-
Spanning Forest of a Graph
- the union of spanning trees of its connected components
-
Spanning Tree of a Connected Graph
- subgraph that contains all of that graph’s vertices subgraph that is a single tree
-
Degree of a Vertex
- number of edges incident to the vertex(loop counts as 2).
-
Predecessor of a Vertex
-
edge(u, v), then vertex v is the descendant of u. Vertex u is the predecessor, or parent/ancestor, of vertex v. v.d is the distance from the source; s.d is 0 when s is the source node. u.d is 1 when the distance from source to u is 1. This is implemented as InVertices in goraph.
-
When Graph G = (V, E) = (Vertex, Edge)
- |V| is the number of vertices in a graph
- |E| is the number of edges in a graph
-
Sparse Graph
- |E| is much less than |V|^2
- Relatively few edges present
-
Dense Graph
- |E| is close to |V|^2
- Relatively few edges missing
-
Adjacency List: good for Sparse Graph
- Use memory in proportion to |E|
- So save memory when G is sparse
- Fast to iterate over all edges
- Slightly slower lookup to check for an edge
-
Adjacency Matrix: good for Dense Graph
- Use O(n^2) memory
- Fast lookups to check for presence of an edge
- Slow to iterate over all edges
func (v *VertexT) GetEdgeTsChannelFromThisVertex() chan *EdgeT {
edgechan := make(chan *EdgeT)
go func() {
defer close(edgechan)
for e := v.OutGetEdge().Front(); e != nil; e = e.Next() {
edgechan <- e.Value.(*EdgeT)
}
}()
return edgechan
}It's not idiomatic Go style to use channels, simply for the ability to iterate over them. It's not efficient, and it can easily lead to an accumulation of idle goroutines: Consider what happens when the caller of GetEdgeTsChannelFromThisVertex discards the channel before reading to the end. It's better to use container/list rather than channel.
I have another Graph Algorithm project written in C++. It is NOT maintained anymore, but if interested check out HERE.
Tree is just another kind of graph data structure. If interested check out gotree.
Tree (a graph G with V vertices) if and only if it satisfies any of the following 5 conditions.
- G has V-1 edges and no cycles
- G has V-1 edges and is connected
- G is connected, and removing any edge disconnects the - G
- G is acyclic, and adding any edge creates a cycle in G
- Exactly one simple path connects each pair of vertices in G