This is the abstract of a talk prepared for the Oeiras Mathematical and Computational Biology Workshop. June 20, 2003, Instituto Gulbenkian de Ciência
Abstract: I will start by present some generic ideas about small-world and evolving networks. Some historical view will also be presented. The Milgram's classic "six degrees of separation" experiments in the 1960's, can be used to show how social network theory has evolved and how individuals interact and disseminate information. I will also focus on networks with complex structure which can describe systems as diverse as biological networks or the Internet. The emergence of these networks is driven by self-organizing processes that are governed by simple but generic laws. I will show that the scale-free topology of real complex webs have important consequences on their robustness against failures and attacks, with implications on drug design, the Internet's ability to survive attacks and failures, etc... I will also present some results about hierarchical networks with applications to biology.