Project Description: In recent years, the structure of complex networks has become object of intense study by scientists from various disciplines; see e.g. [1], [2] and [3], or the book-form paper collection [4]. One often studied mechanism of growth and evolution in such networks, e.g. social networks, is preferential attachment [2]. In communications network engineering, network protocols have been modeled mathematically using tools from optimization [5] and game theory [6]. A picture has emerged of layered networks (modeled as graphs) where each layer of the whole acts non-cooperatively, implicitly optimizing its own objective, treating other network layers largely as a black box. The network layers interact dynamically, and implicit cooperation towards a common overall objective is achieved by a suitable, modular decomposition of tasks to the individual layers. In this project, we will focus on the interaction between social networks and communication networks. Given the communication network, how do social networks grow and evolve? Does preferential attachment account for the structure observed? How do communication networks and their (often protocol-induced) ‘preferences’ affect the structure of social networks, and vice versa? We will use mathematics (optimization, game theory, graph theory) and computer simulation to investigate these questions. Prerequisites: Background: Optimization, Probability, Differential Equations. Computer skills: Matlab, R, Python. References: [1] M.E. Newman, "The Structure and Function of Complex Networks," SIAM Review, Vol. 45, No. 2, pp. 167-256, 2003. [2] L.-A. Barabasi, R. Albert, "Emergence of Scaling in Random Networks," Science, Vol. 286, No. 5439, pp. 509-512, 1999. [3] D.J. Watts, "The ‘New’ Science of Networks," Ann. Rev. Sociology Vol. 30, pp. 243-270, 2004. [4] M.E. Newman, L.-A. Barabasi, D.J. Watts, "The Structure and Dynamics of Networks," Princeton, 2006. [5] M. Chiang, S.H. Low, A.R. Calderbank and J.C. Doyle, "Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures," Proceedings of the IEEE, Vol. 95, No. 1, pp. 255-312, January 2007 [6] E. Altman, T. Boulogne, R. El-Azouzi, T. Jimenez and L. Wynter, "A Survey of Networking Games in Telecommunications," Computers and Operations Research, Vol. 33, No. 2, pp. 286-311, 2006.