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Michael Holroyd
Office: Small Hall
e-mail: meekohi@cs.virginia.edu
AIM: meekohi

self-similar graph Connectivity and Synchronizability of Discrete Complex Systems
This was my honors project my senior year at William and Mary. My advisor was Rex Kincaid from the mathematics department. In addition to receiving high honors for the thesis, I presented and published a paper at the 2006 International Conference on Complex Systems.

Abstract: The synchronization of discrete complex systems is critical in applications such as communication and transportation networks, neuron respiratory systems, and other systems in which either congestion can occur at individual nodes, or system wide synchrony is of importance to proper functionality. The first non-trivial eigenvalue of a network's Laplacian matrix, called the algebraic connectivity, provides a quantifiable measure of synchronizability in a network. We study the general relationship between network topology, clustering coefficient distributions, and synchronizability, as well as the effects of degree preserving rewiring on network synchronizability. In addition, we compare the synchronizability of different network topologies, including Poisson random graphs, geometric networks, preferential attachment networks, and scale-rich networks. We also explore uses of the algebraic connectivity in the design and management of complex networks where synchronization is desired (respiration networks), or detrimental to network performance (router networks).

 Full honors thesis (8.3 MB).
This includes all the source code for the project as well.

 ICCS paper (3.6 MB).
The paper accepted to ICCS 2006.

 ICCS presentation (5.4 MB).
Powerpoint! This is missing a couple video clips, but everything else is there.

Related Publications:

R. Kincaid, N. Alexandrov, M. Holroyd.
An Investigation of Synchrony in Transport Networks. [pdf]
Journal of Complexity 2009, Vol. 14, Issue 4, pp. 34-43.

R. Kincaid, C. Gatz, M. Holroyd.
Understanding the Structure of Power Law Networks. [pdf]
Proceedings of Spring Simulation Multiconference 2007, Vol. 2, pp. 104-111