The definition of a complex network is quite simple: a collection of nodes, with pairs of them connected by links. Things start to get interesting when the number of nodes grows up, when the structure of connections departs from random or regular topologies, or when nodes represent complex dynamical entities, like for instance people in a community. Strange behaviors emerge, and as a consequence, new tools for their analysis: community detection, information spreading algorithms, vulnerability, and so forth.
Biomedical problems, and complex networks
Complex networks allow a non-standard analysis of biomedical problems. For instance, nodes may represent genes, connected if some patterns are found in their expression levels; or they may represent other medical measurements, e.g. metabolic spectra. In all these cases, representing this information by means of complex networks allows extracting relevant knowledge, like the health condition of a patient, the elements most responsible for a given pathology, etc.
When we have a complex network built by customers and items, a new application appears: recommendation systems. And, with each new utility, new problems arise: we want to recommend items to users with the highest precision, and of course we want it fast!
Cryptography is a field that has attracted the attention of mankind since thousand of years: and, of course, mine too. Data and images encryption with chaotic systems is a growing field, with many open issues (e.g. security or computational load) and opportunities.