# Some terms related to the graph theory

Network models are intimately related to a certain branch of mathematics known as the graph theory. Actually networks themselves are graphs! Thus further we briefly introduce some of the terms related to the mathematical graph theory.

In mathematics a **graph** is a collection of **vertices (or nodes)**
that are interconnected by **edges (or links, or arcs)**. Edges might be
either undirected or directed and they also might have weights assigned.

Graphs with directed edges are called **directed** graphs.

Undirected graph can be referred to as **complete** graph, if and only
if every node is connected to all other nodes.

Graph is **empty** if it does not posses any edges.

Edges are considered to be **adjacent** if they connect to one common
node. Nodes are considered to be **adjacent** if they are connected by
an edge.

Node's, in the undirected graph, **degree** is a number of nodes
adjacent to it.

**Chain or path** is a set of the adjacent edges.

**Circuit or cycle** is a path which has the same initial and final
nodes.

**Length** of the path is a number of edges in the path.

Graph H is a **subgraph** of graph G, if H is composed of G nodes and
edges.

H is an **induced** subgraph of G if it has exactly the edges that
appear in G.

Graph is considered to be **connected**, if any pair of nodes is
connected by the path.

**Connected** component of graph G is an induced subgraph of G.

Acyclic graph is called **forest**. Connected forest is called a
**tree**.