Network modeling is based on graph theory.

Graph theory is defined as the study of graphs which are

mathematical structures used to model pairwise relations between objects.

What we mean by graph in this context is

a representation of many nodes connected by edges.

So in practical terms,

this allows for networks to be visualised,

which makes the analysis much easier.

The nodes of a network,

which are sometimes referred to as vertices or points,

correspond to entities, such as proteins or genes in Biological Networks.

The edges of a network,

which are sometimes referred to as arcs or lines,

reveal information about the connections between the nodes.

There are three main types of graphs using Network Modeling:

undirected, directed and weighted.

An undirected graph is a graph in which edges have no orientation or direction.

The relationship between the nodes is simple connection.

The edges indicate a two-way relationship, in that each edge can be bi-directional.

Undirected graphs are commonly found in protein to protein interaction networks.

A directed graph is a graph in which edges have

orientation or a direction associated with them.

The edges indicate a one-way relationship

in that each edge can only go in a single direction.

This means that all the edges are directed from one node to another.

Directed graphs are mainly found in metabolic,

signal transduction or regulatory networks.

Weighted graphs are graphs in which each edge is

given a numerical weight or quantity value.

Such weights might represent, for instance,

sequence or structural similarities between proteins or co-expression of genes.

Weighted graphs can have either directed edges,

one-way relationship or undirected edges, two-way relationship.

All networks can be conveyed mathematically in what is known as Adjacency Matrices.

An Adjacency matrix is a data structure used to store network graph representations.

The values of the Matrix indicate whether

pairs of nodes are adjacent or not in the graph.

More specifically in these matrices,

the nodes in the network are assigned to the rows and columns,

then the connecting edge is given a numerical value.