Graph data can be represented in different formats for onward computation. The choice of the graph representation hugely relies on the density of the graph, space required, speed and weight of edges. The main ways a graph can be represented are as an adjacency matrix, incidence matrix, adjacency list and incidence list.

Adjacency Matrix: This is one of the most popular ways a graph is represented. One of the core aims of this matrix is to assess if the pairs of vertices in a given graph are adjacent or not. In an adjacency matrix, row and columns represent vertices. The row sum equals the degree of the vertex that the row represents. It is advisable to use the adjacency matrix for weighted edges.  You replace the standard ‘1’ with the respective weight.  It is easier to represent directed graphs with edge weights through an adjacency matrix. Adjacency matrix works best with dense graphs. As dense graphs usually have twice the size of the edges to the given nodes.

We are witnessing the rise and adoption of graph databases across different verticals. Gartner acknowledged the five different types of graphs as social, intent, consumption, mobile and interest. In a presentation titled: Graph All the things! Introduction to graph databases, the team from Neo4j captured Gartner’s graph classifications in the illustration below. There is a slight difference in how one of the types of a graph is named by Neo4j in comparison to Gartner. To Neo4j it is a payment graph while to Gartner it is the consumption graph.  There is the argument that a consumption graph is a better name as we do not necessarily pay for every consumption. We will now look at each graph and add some additional types.