Package goraph provides graph visualizing tools and algorithm implementations.
- Getting Started
- Package Hierarchy
- Example
- Testing Graphs
- 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/goraph
goraph/ # Top Package
algorithm/ # Package: Graph Algorithms
bfs/ # Package: Breadth First Search Algorithm
dfs/ # Package: Depth First Search Algorithm
sp/ # Package: Shortest Path Algorithm (Dijkstra, Bellman-Ford)
spbf/ # Package: Shortest Path Algorithm for Negative Edges (Bellman-Ford)
spd/ # Package: Shortest Path Algorithm for Positive Edges (Dijkstra)
spfw/ # Package: Shortest Path Algorithm for Positive Edges (Floyd-Warshall)
tsdag/ # Package: Topological Sort, Detects whether it is a DAG
tsdfs/ # Package: Topological Sort using DFS, Not Detecting DAG
tskahn/ # Package: Topological Sort by Arthur Kahn(1962), Detects DAG
mst/ # Package: Minimum Spanning Tree (Kruskal, Prim)
kruskal/ # Package: Kruskal Minimum Spanning Tree Algorithm
prim/ # Package: Prim Minimum Spanning Tree Algorithm
scc/ # Package: Strongly Connected Component
tarjan/ # Package: Tarjan Strongly Connected Component Algorithm
kosaraju/ # Package: Kosaraju Strongly Connected Component Algorithm
maxflow/ # Package: Maximum Network Flow
fdfk/ # Package: Ford-Fulkerson Maximum Network Flow Algorithm
benchmark/ # Package: Benchmark, Comparison of graph representations
example_files/ # Learn DOT
example_files/ # Files for Example
example_with_script/ # Example Script (Program)
example_with_testing/ # Example Code
goroup/ # Package: Disjoint Set for Graph Nodes
gsdset/ # Package: Set Operation with the package graph/gsd
graph/ # Package: Graph Data Structure
gl/ # Package: Adjacency List, Linked List(container/list), No Duplicate Edges
gld/ # Package: Adjacency List, Linked List(container/list), Allow Duplicate Edges
gm/ # Package: Adjacency List, Map, No Duplicate Edges
gs/ # Package: Adjacency List, Slice, No Duplicate Edges
gsd/ # Package: Adjacency List, Slice, Allow Duplicate Edges
gsdflow/ # Package: Customized gsd for Network Flow Algorithm
gt/ # Package: Adjacency Matrix, Map, No Duplicate Edges
viz/ # Package: Graph Visualization (Graphviz)
dot/ # Package: Convert JSON graph data to DOT- gson: JSON Import Package
- gosequence: Customized Slice(Array) Data Structure
- Graphviz: Graph Visualization
fmt.Println("Dijkstra Shortest Path on testgraph10:")
g10 := gsd.JSONGraph("../example_files/testgraph.json", "testgraph.010")
fmt.Println(spd.SPD(g10, "A", "E"))
fmt.Println(g10.ShowPrev("E"))
fmt.Println(g10.ShowPrev("D"))
fmt.Println(g10.ShowPrev("B"))
fmt.Println(g10.ShowPrev("C"))
fmt.Println(g10.ShowPrev("A"))
/*
A(=0) → C(=9) → B(=19) → D(=34) → E(=36)
Prev of E: C D
Prev of D: B
Prev of B: C
Prev of C: A
Prev of A:
BackTrack keeps adding the Prev vertex
with the biggest StampD, recursively
until we reach the source
*/
println()
fmt.Println("Dijkstra Shortest Path on testgraph10o:")
g10o := gsd.JSONGraph("../example_files/testgraph.json", "testgraph.010")
fmt.Println(spd.SPD(g10o, "E", "A"))
fmt.Println(g10o.ShowPrev("A"))
fmt.Println(g10o.ShowPrev("B"))
fmt.Println(g10o.ShowPrev("C"))
fmt.Println(g10o.ShowPrev("F"))
fmt.Println(g10o.ShowPrev("E"))
/*
E(=0) → F(=9) → C(=11) → B(=21) → A(=22)
Prev of A: F B
Prev of B: C
Prev of C: E F
Prev of F: E
Prev of E:
BackTrack keeps adding the Prev vertex
with the biggest StampD, recursively
until we reach the source
*/func Test_JSON_ShowSPD(test *testing.T) {
g4 := gsd.JSONGraph("../../example_files/testgraph.json", "testgraph.004")
fmt.Println(ShowSPD(g4, "S", "T", "testgraph.004_spd.dot"))
}
func Test_JSON_ShowBFS(test *testing.T) {
g4 := gsd.JSONGraph("../../example_files/testgraph.json", "testgraph.004")
fmt.Println(ShowBFS(g4, g4.FindVertexByID("S"), "testgraph.004_bfs.dot"))
}
func Test_JSON_ShowDFS(test *testing.T) {
g4 := gsd.JSONGraph("../../example_files/testgraph.json", "testgraph.004")
fmt.Println(ShowDFS(g4, "testgraph.004_dfs.dot"))
}
Kruskal Algorithm
func Test_JSON_ShowMST(test *testing.T) {
g14 := gsd.JSONGraph("../../../example_files/testgraph.json", "testgraph.014")
ShowMST(g14, "g14mst_kruskal.dot")
}
Prim Algorithm
func Test_JSON_ShowMST(test *testing.T) {
g14 := gsd.JSONGraph("../../../example_files/testgraph.json", "testgraph.014")
ShowMST(g14, "g14mst_prim.dot")
}
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.
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