Intro Networks and Gephi

Graph theory boils down to places to go, and ways to get there.

A graph refers to a collection of nodes and a collection of edges that connect pairs of nodes.

Nodes: Places to be
Edges: Ways to get there

In the Königsberg example, the land masses and islands are nodes, and the bridges are edges.

Traditional map

Euler’s version

An introduction to networks

Overview of networks

A network is simply a collection of connected objects. We refer to the objects as nodes or vertices, and usually draw them as points. We refer to the connections between the nodes as edges, and usually draw them as lines between points.

Small undirected network with labeled nodes and edgesIn mathematics, networks are often referred to as graphs, and the area of mathematics concerning the study of graphs is calledgraph theory. Unfortunately, the term graph can also refer to a graph of a function, but we won’t use that use of the term when talking about networks. Here, we’ll use the terms network and graph interchangeably.

Networks can represent all sorts of systems in the real world. For example, one could describe the Internet as a network where the nodes are computers or other devices and the edges are physical (or wireless, even) connections between the devices. The World Wide Web is a huge network where the pages are nodes and links are the edges. Other examples include social networks of acquaintances or other types of interactions, networks of publications linked by citations, transportation networks, metabolic networks, and communication networks. You can click on the following images for more information about their respective networks.

Internet map 2004Network of connections between devices within the Internet.

Network of connections between devices within the Internet. Colors indicate operator of network. Structure determined by sending a storm of IP packets out randomly across the network. Each packet is programmed to self-destruct after a delay, and when this happens, the packet failure notice reports back the path the packet took before it died.


Network of US Congress twitterers showing citation frequencyNetwork of US congress twitterers.


Types of networks

When one tries to model systems such as those mentioned above, one quickly realizes that the simple network model with identical nodes and edges cannot describe important features of real networks. One problem is the edges in this simplest network model are undirected.

Small undirected networkAn undirected network.

Small directed networkA directed network.

Small undirected network with different node and edges typesAn undirected network where the nodes and edges have different types, as indicated by their colors and line styles.

Small directed network with weighted nodes and edgesA directed network where the edges and nodes have different weights, as indicated by their sizes.


In some networks, not all nodes and edges are created equal. For example, in metabolic networks, nodes may indicate different enzymes which have a wide variety of behaviors, and edges may indicate vastly different types of interactions. To model such difference, one can introduce different types of nodes and edges in the network, as illustrated by the different colors and edge styles, above. In networks where the differences among nodes and edges can be captured by a single number that, for example, indicates the strength of the interaction, a good model may be a weighted graph. One can represent a weighted graph by different sizes of nodes and edges.

In some contexts, one may work with graphs that have multiple edges between the same pair of nodes. One might also allow a node to have a self-connection, meaning an edge from itself to itself. An example of such a network is shown, below.

Small undirected network with multiple edges and self-connectionsFor simplicity, we will focus primarily on unweighted graphs with a single type of node and a single type of edge. We will consider both directed and undirected graphs, but won’t allow multiple connections or self-connections.




Creating a Network Graph with Gephi


Exploratory Data Analysis: intuition-oriented analysis by networks manipulations in real time.

Link Analysis: revealing the underlying structures of associations between objects.

Social Network Analysis: easy creation of social data connectors to map community organizations and small-world networks.

Biological Network analysis: representing patterns of biological data.

Poster creation: scientific work promotion with hi-quality printable maps.