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https://github.com/jonghough/sharpgraph

C# Graph Library
https://github.com/jonghough/sharpgraph

graph graph-algorithms mathematics

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C# Graph Library

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README 

        
 

# SharpGraph

 

 A C# Library Package for `.Net 6` and above, for the purpose of working with graphs and  graph algorithms.



![unit test workflow](https://github.com/jonghough/SharpGraph/actions/workflows/unit-test.yaml/badge.svg?branch=master)

 

## Project

This is a .NET library containing an assortment of graph algorithms.



## Nuget

```

dotnet add package SharpGraphLib --version 1.0.1

```



#### Some currently implemented algorithms:



| Algorithm | Usage |

|---------------------------------|----------------------------------------------------|

|Dijkstra | for finding shortest path between two nodes on a connected weighted graph, with non-negative weights|

|A-Star | for finding shortest path between two nodes on a connected weighted graph, with non-negative weights - usually faster than Dijkstra|

|Cycle finding | find all cycles on a given graph. Find Hamiltonian cycles.|

|Bellman-Ford | for finding shortest path between two nodes on a connected, weighted graph with positive or negative weights, and no negative weight cycles|

|Spanning Tree | finds the minimum spanning tree for a connected, weighted graph|

|Connected subgraphs | find all maximally connected subgraphs of a graph|

|bionnected subgraphs | find all biconnected subgraphs of a graph|

|General DFS and BFS search algorithms | For graph searching |

|Find minimum cut of a graph | Necessary edges to keep the graph connected|

|Maximum Flow | Find max flow in a flow network |

|Planarity testing | Checks if a graph is planar |



 

## Example usage



We can create a graph by specifying the edges and labeling nodes as below.



```csharp

Edge eAB = new Edge ("A","B");

Edge eAC = new Edge ("A","C");

Edge eCD = new Edge ("C","D");

Edge eDE = new Edge ("D","E"); 

Edge eAF = new Edge ("A","F"); 

Edge eBF = new Edge ("B","F"); 

Edge eDF = new Edge ("D","F"); 



List list = new List ();

list.Add (eAB);

list.Add (eAC);

list.Add (eCD);

list.Add (eDE);

list.Add (eAF);

list.Add (eBF);

list.Add (eDF);



Graph g = new Graph (list); 

```



### create a complete graph (graph where all nodes are connected to each other)



```csharp

//first create  10 nodes

var nodes = NodeGenerator.GenerateNodes(10);



// this will create a complete graph on 10 nodes, so there are 45 edges.

var graph = GraphGenerator.Create(nodes);

```



### is the graph connected?



```csharp

//test whether the graph is connected, which means it is possible to move from any point to any other point.

var g = new Graph():

for(int i = 0; i < 10;i++){

    g.AddEdge(new Edge(""+i, ""+(i+1)));

}

g.IsConnected(); //true

```

As another exampler, we can generate a complete graph on 10 nodes and check if it is connected. We can also

find biconnected components of the graph.

```csharp

var g = GraphGenerator.CreateComplete(NodeGenerator.GenerateNodes(10)); // generate complete graph

g.IsConnected(); //true

//find biconnected components

g.FindBiconnectedComponents (); // complete graph so only 1 biconnected component, the graph itself.

```



### find minimum spanning tree of a connected weighted graph



```csharp

Node b1 = new Node ("1"); 

Node b2 = new Node ("2"); 

Node b3 = new Node ("3"); 



Edge wedge1 = new Edge (b1, b2);

Edge wedge2 = new Edge (b1, b3);

Edge wedge3 = new Edge (b2, b3);

var edges = new List ();

edges.Add (wedge1);

edges.Add (wedge2);

edges.Add (wedge3);



var g = new Graph (edges);



g.AddComponent (wedge1).Weight = -5.1f;

g.AddComponent (wedge2).Weight = 1.0f;

g.AddComponent (wedge3).Weight = 3.5f;

var span = g.GenerateMinimumSpanningTree ();



```



### find ALL cycles in a graph (this algorithm is very slow, don't use for big graphs)



#### example

![cycles](/graph_cycles.png)



In the above graph there are 3 basic cycles. This is easily calculated. For more complicated graphs the

calculation can be quite complex. For example, for the complete graph on 8 nodes, there are 8011 cycles to find.



```csharp

HashSet nodes7 = NodeGenerator.GenerateNodes(7);

var graph7 = GraphGenerator.CreateComplete(nodes7); 

var cycles = graph7.FindSimpleCycles();

// number of cycles should be 1172

```



### find shortest path between two nodes on a *weighted graph*



We can find the minimum distance path between any two nodes on a connected graph using `Dijkstra's Algorithm`. 



```csharp 

Edge eAB = new Edge ("A", "B");

Edge eAG = new Edge ("A", "G");

Edge eCD = new Edge ("C", "D");

Edge eDH = new Edge ("D", "H");

Edge eAF = new Edge ("A", "F");

Edge eBF = new Edge ("B", "F");

Edge eDF = new Edge ("D", "F");

Edge eCG = new Edge ("C", "G");

Edge eBC = new Edge ("B", "C");

Edge eCE = new Edge ("C", "E");



List list = new List ();

list.Add (eAB);

list.Add (eAG);

list.Add (eCD);

list.Add (eDH);

list.Add (eAF);

list.Add (eBF);

list.Add (eDF);

list.Add (eCG);

list.Add (eBC);

list.Add (eCE);



Graph g = new Graph (list);



g.AddComponent (eAB).Weight = 10;

g.AddComponent (eAG).Weight = 14;

g.AddComponent (eCD).Weight = 5;

g.AddComponent (eDH).Weight = 5.5f;

g.AddComponent (eAF).Weight = 12;

g.AddComponent (eBF).Weight = 3.5f;

g.AddComponent (eDF).Weight = 1.5f;

g.AddComponent (eCG).Weight = 11.5f;

g.AddComponent (eBC).Weight = 6.5f;

g.AddComponent (eCE).Weight = 6.5f;



List path = g.FindMinPath (b1, b8);



```



### find shortest path between two nodes on a *weighted graph* with A-Star



For a faster algorithm, we can use the `A-star algorithm` to find the minimum path on the same graph as above.



```csharp 

List path = g.FindMinPath (b1, b6, new TestHeuristic (5));



```

 

## Design



There are four main objects:



### Graph 

an object which contains collections of *edges* and *nodes*. Most algorithms and functionality are Graph methods in this design. Graphs can be copied and merged.



### Edge 

contains pairs of *Nodes*. Can be associated with any number of *EdgeComponent*s. Comparison of Edges is based on whether their nodes are identical.

### Node

In a given graph, a node (or *vertex*) must have a unique name, a label, that defines it.  



### Components

Edges and Nodes share a similar *Component* architecture, where a given edge may have attached to it multiple `EdgeComponent` subclass instances. Similarly, Nodes can have multiple

`NodeComponent` subclass instances attached to them.



In  this way, we can define weight edges as a new component `MyEdgeWeight`, which can contain a `float` value (the weight), and attach this component to each edge of our graph. This is simpler than having a subclass of `Edge`, `WeightedEdge` and having  web of generics in the library. It is also very flexible and allows pretty much any type of `Node` or `Edge` type without creating subclasses. Just define our component and attach it to each edge / node. 



For example, a *Directed Graph* is just a graph with a *DirectionComponent* attached to each edge in the graph. 



## testing



In the base directory

```

dotnet test ./

```



## building

see [dotnet link](https://learn.microsoft.com/en-us/dotnet/core/tools/dotnet-build)

```

dotnet build --configuration Release

```