The purpose of this thesis was to explore some elementary notions of thermodynamics, like extensivity and the thermodynamic limit, in the context of complex networks and with regard to the fact that standard physical quantities and objects, like volume or particles, upon which the definitions, or at least the intuition, of said notions usually depend do not exist in networks (graphs). The result is the conclusion that the notion of a particle, in the sense of an elementary part of a system, is central for the definition and interpretation of other thermodynamical notions. As a consequence of this conclusion two views, i.e. thermodynamical pictures, were developed: vertices-as-particles and edges-as-particles, which were then applied to the basic statistical models of complex networks. It was determined that various properties of models, like ensemble equivalence and additivity, differ greatly depending on the chosen picture and that the edges-as-particles picture gives consistent and mathematically sound results while the vertices-as-particles picture does not. It was also determined that some of the current results, like the inequivalence of ensembles of the configuration model and the conclusion that additivity does not determine ensemble equivalence, were acquired effectively in the frame of the vertices-as-particles picture and are thus invalid. At the same time, other work and results in the area of statistical models of networks, mostly by mathematicians, were found in line with the edges-as-particles picture which now provides them with a conceptual grounding and physical support.