Simple and lightweight C++ implementation for oriented adjancency matrices
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Simple and lightweight C++ implementation for oriented adjancency matrices.

## What's that?

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. -- Wikipedia

The original graph consists in nodes (aka vertices), connected to others by a set of edges. In directed graphs, the so-called oriented adjacency matrix indicates wheter each edge is walked by forward or backward; hence, it is skew-symmetric.

### Example

Here is an example graph:

Its consists in vertices (rounded nodes) and oriented edges (arrows). The corresponding adjacency matrix is:

## How to use

### Install

Just put the `.h` and `.cpp` files in the working directory, and add the following line in the file where you want to use the adjacency matrix:

``````#include "adjacencyMatrix.h"
``````

## Examples

### Create a new instance of adjacency matrix

``````adjacencyMatrix adj_mat;
``````

Note that the size of the matrix is not mandatory here, since it will be dynamically computed (see below). If the size of the matrix is already known, it can passed to the constructor:

``````adjacencyMatrix adj_mat(7);
``````

### Add a new entry in the adjacency matrix

``````int id1=1,id2=2;
``````

A unique ID is automatically associated to the new edge (starting from 1, incrementing by 1 each time a new entry is added). If necessary, the size of the matrix is dynamically increased.

### Check if an edge exists between node id1 and node id2

``````adj_mat.get(id1,id2);
``````

### Check if an edge exists between node id1 and node id2 and get the corresponding edge ID

``````int ide;
``````

### Display the adjacency matrix

``````adj_mat.print();
``````

## How it works

Since the oriented adjacency matrices are skew-symmetric, data are stored as lower triangular matrices, in a sake of memory.

## Notes

### Self loop

Because of the skew-symmetry, self loops are forbidden in oriented adjacency matrices. Hence, the diagonal is always zero.

### Negative node indices

If any input argument of `Set` is negative, no entry is added to the matrix. Still, the maximum edge ID is incremented. The same behaviour applies for equal indices (see above).

### Purpose

The class was designed for the voroGmsh class.