  A book Chapter consisting of some of the main areas of research in graph
theory applied to physics. It includes graphs in condensed matter theory, such
as the tight-binding and the Hubbard model. It follows the study of graph
theory and statistical physics by means of the analysis of the Potts model.
Then, we consider the use of graph polynomials in solving Feynman integrals,
graphs and electrical networks, vibrational analysis in networked systems and
random graphs. The second part deals with the study of complex networks and
includes the models of "small-world", "scale-freeness", network motifs,
centrality measures, the use of statistical mechanics for the analysis of
networks and network communicability and the study of communities in networks.
The chapter is finished by considering some dynamical models on networks, such
as the consensus analysis, synchronization of coupled oscillators and epidemic
models on networks.
