Network properties

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.