Version: 1.1

GraphJS is a library designed to facilitate computation within the context of Graph Theory for Javascript (currently in development). For a demo implemented using p5.js click [here](https://delsquared.github.io/GraphJS/). (Rough knowledge of the browser console is required)

Here is a screenshot of the demo. The central diagram is the graph and the diagram at the bottom left is a representation of the adjacency matrix of said graph:

Importing

To include in your HTML, use the following line:
<script src="https://cdn.rawgit.com/DelSquared/GraphJS/817b5539/lib/Graph.js" type="text/javascript"></script>

Matrix Commands

nullMatrix(n): Creates an n x n matrix of zeros

SumM(A): Sums over all the entries of A

det(A): Returns the determinant of A (Temporarily removed due to buggy and poor implementation)

Tr(A): Returns the trace of A

Trans(A): Returns the transpose of A

Add(A,B): Adds matrices A and B

Subt(A,B): Subtracts B from A

Mult(A,B): Multiplies A onto B

MultTrans(M): Multiplies M onto its transpose. Use MultTrans(Trans(M)) to reverse multiplication order

Graphs

Edge-Related Commands

Edge (u,v): Creates an "edge" object taking in incident vertices u and v

randomEdges(maxE,n): Returns an array of Edge objects for a random graph on n vertices with maxE as a max number of edges

cyclicEdges(n): Returns an array of Edge objects for a cyclic graph on n vertices (C_n)

completeEdges(n): Returns an array of Edge objects for a complete graph on n vertices (K_n)

completeBipartiteEdges(n,p): Returns an array of Edge objects for a complete-Bipartite graph on n vertices with partitions p and n-p (K_p,n-p)

petersen10Edges(): Returns an array of Edge objects for the Petersen-10 graph. Note that in the Graph constructor the argument n=10 is mandatory to get the exact Petersen graph with no added disconnected vertices.

Graph Object

Arguments: (n,edgeList) where n is the number of vertices and edgeList is an array of Edge objects one can pass the edge-list functions directly into the constructor to get a particular graph, alternatively one can construct an array entirely from scratch.

Attributes:

Graph.adjacencyMatrix: The adjacency matrix constructed from the edge list compactly storing all information about the connections of the vertices

Graph.n: The number of vertices of the graph

Graph.m: The number of edges of the graph

Graph.degreeMatrix(): A method that returns the degree matrix of the graph

Graph.laplaceMatrix(): A method that returns the Laplace matrix of the graph

Graph.incidenceMatrix(): A method that returns the incidence matrix of the graph

Graph.swapVertexLabel(u,v): A method that gives an automorphism of the graph by swapping the label of the two given vertices u and v

Planned Future Additions

• A separate p5.js wrapper library to facilitate drawing and visualisation. Ideal for teaching.

• Graph colouring algorithms.

• Implement more matrix representation like the Seidel Matrix, etc.

• Implement more Linear Algebra concepts like spectra, determinant, characteristic polynomials, etc.

• Including Typescript in order to speed up the code by having fixed variable types.

• Possible WebGL inclusion to accelerate matrix calculations.