Networks are ubiquitous: We are ourselves nodes of social networks and results of the subtle interplay of different biological regulation networks.
Complex networks have become a paradigm. Indeed the last eight years have seen the publication of a large number of papers in the physics and mathematics literature. Networks of various kinds have been analyzed, particularly computer and information networks like the Internet and the WWW, biological networks such as food webs, neural networks, metabolic networks, genetic regulatory networks, technological, linguistic and social networks.
When looking at networks from the point of view of complex systems, the focus is placed on the microscopic processes that rule the appearance, disappearance and state of vertices and edges. Since the system is composed of very many interacting vertices (units, agents, …) a detailed analysis of the dynamics of each node is difficult and avoided in favour of the understanding of the cooperative phenomena originated by the microscopic interactions and the statistical laws governing the system.
This viewpoint allows to use well known techniques of statistical physics such as percolation theory, mean field approximation, Markov fields and associated dynamics, cellular automata simulations, renormalization group …. One reason that graph theory is interesting is because it reflects the structure of human thinking. Indeed the human minds think about relations between things or agents. Relations integrate the objects into a network. In adaptive systems the relations change in time in such a way that the connectivity of the graph may change.
The focus of theoretical research in this fields splits into three main directions:
The role of graph theory is of particular significance in our understanding of the mathematics governing the discrete universe in all branches of natural, social and life science. An important reason for the interest in Random Graph Theory and Complex Networks is the relevance to real-world problems. The objectives and the covered topics are clearly interdisciplinary. More precisely the workshop addresses various scientific communities for which Complex Networks are a common subject of interest. These include physicists and mathematicians working on disordered systems and interacting particle systems, computer scientists, theoretical biologists, engineers, epidemiologists, applied mathematicians and physicists working in social science and microscopic modelling of financial markets, scientists working on learning or aesthetic networks, including linguists, psychologists and philosophers.The focus of the talks splits into four areas:
The workshop was organized in the frame of VW-Project "Network formation rules, random set graphs and generalized epidemic process" and of the DFG-International Training Group 1132 "Stochastic and Real World Problems" and had reserved enough time for discussion and interaction among attendants. The success of the conference was due first of all to the speakers. Thanks to their efforts, it was possible to take into account recent developments as well as open and to make this interdisciplinary conference an exciting meeting.