Thesis Committee: Joshua Socolar, Henry Greenside, Ronen Plesser, Calvin Howell (exofficio non-voting member)
ABSTRACT: This project studies the structure the relationship
between structural and dynamical features of networks. We create a
model of network growth based on growth rules inspired by biology,
proposed by Socolar and Kauffman. We then use analytical tools as well
as simulations to explore the structural properties of networks formed
by
this model, such as degree distribution and clustering coefficient. Our
goal is to see how
much biologically plausible structure can be created by simple rules,
without the careful crafting of natural selection. We find a broad
range of possible behaviors exhibited by our model for different
parameter values. We also explore a measure of the feedback loop
structure of networks
proposed by Socolar. We believe this measure captures important global
features of the network
that are essential to its dynamical behavior. We implement an algorithm
in Mathematica for
measuring this structure and apply it to several different classes of
networks. We find that
networks formed by preferential attachment produce fewer feedback loops
than NK networks.
Here is the thesis in PDF: dfoster_thesis.pdf (about 0.31 MBytes)