Eleanor Davis
The study of networks stretches across all areas of life: networks can be used to model systems
ranging from social interaction (human or otherwise) to the electrical grid. The vast majority of
real networks are either reciprocal (mutual links occuring more often than random) or
antireciprocal (mutual links occuring less often than random). However, analytical difficulty has
limited most models to use areciprocal networks, where mutual links are completely random. I
have been in studying directed networks which give rise to the synchronization phenomenon: an
important area that has received limited attention. Synchronizability is often a desired aspect of
networks. Improving it can have many applications, including increased understanding of
intercellular communication and improved stability of power networks. To analyze the
synchronizability, I have been examining the eigenvalues of the Laplacian matrix. The change in
the standard deviation of eigenvalues for varying levels of network reciprocity show the
changing ease of synchronizability.