Ελληνικά-Greek English-Αγγλικά
Graduate Course at the Mathematics Department
NETWORKS
2003-4 Spring Semester
Instructor: assoc. prof. Μ.A. Boudourides

SHORT DESCRIPTION

The aim of this course is to offer a detailed overview of the theory of complex networks, a relatively new field, the study of which has started during the last years. Undoubtedly, the interest in complex networks has followed the growth - mainly during the last decade - of computer networking on a global scale, as it is manifested by the Internet and the World-Wide Web (or Web). Furthermore, a large number of other applications of complex networks has appeared in many fields, as in sociology, economics, biology, physics etc. Therefore, it is urgently important for theorists to comprehend the distinctive characteristics of complex networks through a variety of perspectives, as in structural-static analysis, in dynamic (time-dependent) behavior and in studies of networked (non-linear) dynamical systems.

In particular, we are going to cover six areas around complex networks. First, we are going to study the 'small world' properties, which in a sense place complex networks somewhere in between regular lattices and random graphs. Although small world networks have been known to social scientists since the 1960s, during the last years they have been found in a growing number of different cases, as in the Web and networks of scientific collaboration. Moreover, two important characteristics found in complex networks are that these networks are scale-free and that various attributes are distributed on these networks according to non-linear power laws. In this way, studying the graph structure of the Internet, one is able to discern that these types of non-linear behavior abound in a broad range, from the Internet topology to the World-Wide Web and e-mail networks. By understanding the structure and the dynamics of complex networks, one is able to implement more efficient methods and algorithms of search on such networks. Finally, we are interested in analyzing a group of diffusion phenomena occurring on complex networks, as in epidemics, viruses, spamming etc.; thus, we intend to study those mechanisms generating heterogeneous patterns over the network and implying their propagation or effacement or emergence of diverse equilibrium patterns.

SYLLABUS

Note: Readings followed by (*) are compulsory - others are recommended but optional.
  1. Small World Networks
  2. Small Worlds in WWW, Society and Scientific Collaboration
  3. Scale-Free Networks and Power Laws
  4. Power Laws in WWW and the Internet
  5. Search in Networks
  6. Diffusion in Networks
MAILING LIST

USEFUL SOFTWARE

SITES OFRELATED COURSES

USEFUL RESOURCES