Complex Networks

1 Course Unit

The course covers the methodological foundations of network formation and utilization. It introduces various mathematical models for random and strategic, static and dynamic formation of networks. The models for random static formation span, Erdos Renyi Graphs and Power law topologies. Threshold properties underlying these formations will be rigorously proved. The dynamic formations will introduce mean field based deterministic models for network evolution. Techniques for approximately analyzing various key network features such as component sizes will be introduced. These analyses will culminate in tools for approximate analysis of efficacy of various immunization strategies considering epidemic disease spread over networks. A solid background in undergraduate probability is required (e.g. ESE 3010, STAT 4300, ENM 3210, CIS 2610 or equivalent). Spring Mutually Exclusive: ESE 5010 Prerequisites: Students must take ESE 3010 before taking ESE 4010. 1 Course Unit