Network Properties

Graphs are widely adopted in different research fields, since they can model a wide variety of relations and structures, both in bioinformatics and in systems biology. Many analyses of biological networks take advantage of graphs to achieve their results. For this reason, a good understanding and knowledge of mathematical properties of graphs is fundamental to understand their structure. In this contribution, 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 complete graphs, and on the density measure, to determine the degree of connection of graphs. This latter measure will also allow to distinguish between highly connected graphs, called dense graphs, and poorly connected ones, called sparse graphs.