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. A network with undirected and unweighted edges are simple connections. Therefore, its adjacency matrix is simply represented by a symmetric matrix containing only the values one and zero. These values simply indicate the presence or absence of connections respectively. Directed and weighted networks have more complex relationships, and so can use different numerical values in the matrix to illustrate this. These values are sometimes used to indicate stimulation or inhibition within a network. The way in which nodes and edges are arranged within a network is down to its topology. Topological properties can help to identify relevant sub-structures within a network. These properties can be applied to the entire network or to individual nodes and edges. An example of a topological property is the degree of a network. A degree of a network is a number of edges that connect to node. Therefore, directed network nodes have two values for degree, an out-degree for those edges coming out of the node and an in-degree for those edges coming into the node. In the next video, we're going to have a look at the most common types of biological networks.