Abstract

Many real-world networks also exhibit a variety of symmetries. In this thesis we study equitable partitions and isospectral reductions, both of which are generalizations of symmetries. We formalize the relationship between these two types of generalized symmetry through the study of invariant subspaces. We then use recent results about the presence of equitable partitions in real-world networks to develop a network growth model that introduces similar structures, thereby introducing symmetries similar to those in real world networks.

Degree

College and Department

Mathematics; Computational, Mathematical, and Physical Sciences

Rights

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