Spectral theory of networks: from biomolecular to ecological systems

The best way for understanding how things work is by understanding their structures [1]. Complex networks are not an exception [2]. In order to understand why some networks are more robust than others, or why the propagation of a disease in faster in one network than in another is necessary to understand how these networks are organized [3-5]. A complex network is a simplified representation of a complex system in which the entities of the system are represented by the nodes in the network and the interrelations between entities are represented by means of the links joining pairs of nodes [3-5]. In analyzing the architecture of a complex network we are concerned only with the topological organization of these nodes and links. That is to say, we are not taking care of any geometric characteristic of the systems we are representing by these networks but only on how the parts are organized or distributed to form the whole system.