The Structure of Complex Networks

Ernesto Estrada obtained a PhD in Mathematical Chemistry from the Central University of Las Villas, Cuba in 1997 and completed post-doctoral studies at the University of Valencia, Spain and the Hebrew University of Jerusalem, Israel. In 2008 he was appointed Professor and Chair in Complexity Science at the Department of Mathematics and Statistics and the Department of Physics, University of Strathclyde, Glasgow, U.K. In 2005 he was elected fellow of the International Academy of Mathematical Chemistry (IAMC) and in 2007 he received the IAMC award as Outstanding Scientist for his multidisciplinary research in the field of complex networks. Estrada has published more than 140 scientific papers and has made seminal pioneering contributions in the areas of network matrix functions, communicability, bipartivity, subgraph centrality, generalised topological indices and the so-called Estrada index of a network.

1. Introduction ; 2. Adjacency Relationships in Networks ; 3. Metric and Topological Structure of Networks ; 4. Fragments (Subgraphs) in Complex Networks ; 5. Accounting for all parts (subgraphs) ; 6. Communicability Functions in Networks ; 7. Centrality Measures ; 8. Global Network Invariants ; 9. Expansion and Network Classes ; 10. Community Structure in Networks ; 11. Network Bipartivity ; 12. Random Models of Networks ; 13. Genetic Networks ; 14. Protein Residue Networks ; 15. Protein-protein Interaction Networks ; 16. The Structure of Reaction Networks ; 17. Intercellular Networks ; 18. Networks in Ecology ; 19. Socio-Economic Networks ; 20. Conclusions