Statistical and Machine Learning Approaches for Network Analysis

2.2 Representation of Networks

Networks are represented as sets of nodes and edges drawn between the nodes; thus, networks are essentially similar to “graphs” in mathematics. Examples of networks representing real-world systems are listed in Table 2.1.

Table 2.1 Examples of Nodes and Edges in Networks Based on Ref. [4]

Network	Nodes	Edges
Internet	Computer or router	Cable or wireless data connection
World Wide Web	Web page	Hyperlink
Citation relationship	Article, patent, or legal case	Citation
Power grid	Generating station or substation	Transmission line
Friendship network	Person	Friendship
Metabolism	Metabolite	Metabolic reaction
Food web	Species	Predation

There are several types of networks (graphs); the major types are shown in Figure 2.1.

Figure 2.1 Examples of small networks: a simple network (a), a directed network (b), and a weighted network (c) in which the numbers along the edges correspond to the weights. The integers in circles correspond to the labels for nodes.

In the simplest case, networks are represented as shown in Figure 2.1a. The relationship (or interaction) between two given nodes is represented in a network by drawing edges between the nodes. In this case, multiedges, which refer to multiple edges between the same pair of nodes, and self-edges, in which the source is identical to the target, are neglected for simplicity. However, the above-mentioned ...