Network Mathematics: Why is it a Small World?

Presented at DEF CON 15 (2007), Aug. 5, 2007, 11 a.m. (50 minutes)

Networks are central do almost everything that hackers do. Be they computer networks, peer-to-peer networks, information networks, or social networks, they are all around us and understanding them is the key to understanding both the strengths and vulnerabilities of our world. The speaker, a mathematician working in the field of complex networks, will introduce the modern mathematics of networks, and how it can be applied to real-world situations. In particular, we will look at the small-world phenomenon, which says that points in many naturally occurring networks tend to separated in only a few steps. In the case of social networks formed by friendship bonds, this is the famous "six degrees of separation". We will discuss the relevance of this to the world around us, as well as attempt an understanding of the dynamics of such networks, what makes them special, and why they seem to form naturally without explicit design.

Presenters:

  • Oskar Sandberg - Chalmers Technical University and GĖ†teborg University
    Oskar Sandberg (born 13 January 1980 in Falun, Sweden), is a key contributor to the Freenet Project, and a graduate student at the Chalmers Technical University in Gothenburg, Sweden. Oskar collaborated with Ian Clarke to design the new "darknet" model employed in Freenet 0.7, work which was presented at the DEF CON security conference in July 2005. Oskar is also working on a Ph.D. about the mathematics of complex networks, especially with regard to the small world phenomenon. Besides this he has an active interest in distributed computer networks and network security, and has been an active contributor to the Freenet Project since 1999.

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