Handbook of graphs & networks : from genome to the internet

Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

Bela Bollobas and Oliver Riordan: 1. Random Graphs Mark Newman: 2. Random Graphs as Models of Networks Albert-Lázló Barabási: 3. Emergence of Scaling in Complex Networks R. Cohen, S. Havlin, and D. ben-Avraham: 4. Structural Properties of Scale-Free Networks Romualdo Pastor-Satorras and Alessandro Vespignani: 5. Epidemics and Immunization in Scale-free Networks Ralf J. Sommer: 6. Cells and Genes as Networks in Nematode Development and Evolution Ricard V. Solé and Romualdo Pastor-Satorras: 7. Complex Networks in Genomics and Proteomics Sergei Maslov, Kim Sneppen and Uri Alon: 8. Correlation Profiles and Motifs in Complex Networks Wolfgang Kinzel: 9. Theory of Interacting Neural Networks B. Drossel and A. J. McKane: 10. Modelling Food Webs Kai Nagel: 11. Traffic Networks Alan Kirman: 12. Economic Networks Lada A. Adamic, Rajan M. Lukose and Bernardo A. Huberman: 13. Local Search in Unstructured Networks S.N. Dorogovtsev and J.F.F. Mendes: 14. Accelerated Growth of Networks Gérard Weisbuch and Sorin Solomon: 15. Social Percolators and Self Organized Criticality Sanjay Jain and Sandeep Krishna: 16. Graph Theory and the Evolution of Autocatalytic Networks Themes in biological networks are: regulatory networks in the genome, protein networks in the living cell, neural networks, ecological networks and food webs, epidemic networks. Further themes are: communication networks, internet and the World-Wide Web, peer-to-peer networks, computer viruses, traffic networks, social networks. Methods: network growth models, scale-free networks, small-world networks, autocatalytic networks, generalized random graphs, graph theory of random graphs, percolation on networks.