The aim of this review is to tackle questions raised by today's increasing demands and aid researchers in understanding the graph theory behind the biomedical networks as well as concepts such as visualization, annotation, management, clustering, integration, etc. While most recent review articles focus on biomedical and biological networks and their applications ( McGillivray et al., 2018 Sonawane et al., 2019 Yue et al., 2019), in certain case studies, familiarity with the graph theory concepts behind these networks is often missing. We expect this review to reach a very broad spectrum of readers varying from experts to beginners while encouraging them to enhance the field further. Finally, we discuss a variety of algorithms and metrics for network analyses regarding graph drawing, clustering, visualization, link prediction, perturbation, and network alignment as well as the current state-of-the-art tools. We briefly mention the network patterns, motifs and models, and we further comment on the types of biological and biomedical networks along with their corresponding computer- and human-readable file formats. In addition, we describe several network properties and we highlight some of the widely used network topological features. In this article, we discuss the basic graph theory concepts and the various graph types, as well as the available data structures for storing and reading graphs. Networks are one of the most common ways to represent biological systems as complex sets of binary interactions or relations between different bioentities. 3Lawrence Berkeley National Laboratory, Department of Energy, Joint Genome Institute, Walnut Creek, CA, United States.2Department of Informatics and Telecommunications, University of Athens, Athens, Greece.1Institute for Fundamental Biomedical Research, BSRC “Alexander Fleming”, Vari, Greece.Mikaela Koutrouli 1 †, Evangelos Karatzas 1,2 †, David Paez-Espino 3 and Georgios A.