# Graph Theory — Set & Matrix Notation

The first example graph we’ll review contains specific properties that classify it as a simple graph..Two main types of matrix setups are industry-practice: adjacency matrices & incidence matrices.Adjacency MatrixConnected vertices are known as neighbor, or adjacent to one another..Every item in an adjacency matrix is simply a Boolean that describes connectivity.In an adjacency matrix, the graph G with the set of vertices V & the set of edges E translates to a matrix of size V²..Let’s go ahead & transcribe our example graph as an adjacency matrix below:Incidence MatrixThe second common syntax for transcribing graphs as matrices is through an incidence matrix..In an incidence matrix, the graph G with the set of vertices V & the set of edges E translates to a matrix of size V by E..For one, since there are always more edges than vertices, it follows that adjacency matrices have fewer columns than incidence matrices..Lastly, adjacency matrices always follow a square-matrix pattern while incidence matrices are much more likely to represent a rectangle.The key difference is that in former rows & columns represent vertices, while in the latter, rows & columns represent vertices & edges respectively.Past Simple GraphsWith basic notation now out of the way, it’s time to move on studying fundamental graph properties that are commonly used to describe different types of graphs.. More details