Graphs and Networks

Catalog description

Selected topics about the mathematics of graphs and networks with an emphasis on random graph models and the dynamics of processes operating on these graphs. Topics include: empirical properties of biological, social, and technological networks (small-world effects, scale-free properties, transitivity, community structure); mathematical and statistical models of random graphs and their properties (Bernoulli random graphs, preferential attachment models, stochastic block models, phase transitions); dynamical processes on graphs and networks (percolation, cascades, epidemics, queuing, synchronization). Prerequisites: Multivariable calculus; Linear algebra; APMA 0355 or equivalent; APMA 1655 or equivalent; programming experience. APMA 1200 or APMA 1690 or similar courses recommended.