Graphs are widely adopted in different research fields, since they can be used to model a wide variety of relations and structures, in both bioinformatics and systems biology. In fact, the majority of the analysis of biological networks take advantage of graphs to achieve their results. For this reason, a good understanding and knowledge of these mathematical structures is fundamental. In this work, we will review the main properties of graphs related to the degree of vertices, that is, the number of edges incident on them, by giving the formal definitions and proposing different examples. We will also focus on a specific type of graphs, namely the complete graphs, and on the density measure, to determine the degree of connection of the graphs. This latter measure will also allow to distinguish between the highly connected graphs, called dense graphs, and the poorly connected ones, called sparse graphs.

Beretta, S., Denti, L., Previtali, M. (2019). Network properties. In Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics (pp. 928-932). Elsevier [10.1016/B978-0-12-809633-8.20422-6].

### Network properties

#### Abstract

Graphs are widely adopted in different research fields, since they can be used to model a wide variety of relations and structures, in both bioinformatics and systems biology. In fact, the majority of the analysis of biological networks take advantage of graphs to achieve their results. For this reason, a good understanding and knowledge of these mathematical structures is fundamental. In this work, we will review the main properties of graphs related to the degree of vertices, that is, the number of edges incident on them, by giving the formal definitions and proposing different examples. We will also focus on a specific type of graphs, namely the complete graphs, and on the density measure, to determine the degree of connection of the graphs. This latter measure will also allow to distinguish between the highly connected graphs, called dense graphs, and the poorly connected ones, called sparse graphs.
##### Scheda breve Scheda completa Scheda completa (DC)
Capitolo o saggio
Complete graph; Dense graph; Graph density; Node degree; Sparse graph;
English
Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics
6-set-2018
2019
978-0-12-811432-2
1
Elsevier
928
932
Beretta, S., Denti, L., Previtali, M. (2019). Network properties. In Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics (pp. 928-932). Elsevier [10.1016/B978-0-12-809633-8.20422-6].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/311012
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