Networks

Networks are a data structure that consists of a set of nodes (vertices) and a set of edges that relate the nodes to each other. The set of edges describes relationships among the vertices. Graphs are used to model many real-world systems, including computer networks, social networks, and transportation systems.

There are two common ways to represent a graph as a matrix: 1. Adjacency Matrix and 2. Edge List.

The first way is to use an Adjacency matrix, which is a matrix where each row and column represents a vertex. If there is an edge from vertex \(i\) to vertex \(j\), then the entry in row \(i\) and column \(j\) is 1. Otherwise, the entry is 0. For example, the following matrix represents a graph with 4 vertices and 4 edges:

The second way to represent a graph as a matrix is to use an Edge list. An edge list is a list of pairs of vertices that are connected by an edge. For example, the following edge list represents the same graph as the adjacency matrix above: