Abstract by Benjamin Burt
Spectral measures for network similarity
A network can be used to represent anything with relations between discrete objects. Friendships and rivalries between friends, webpages on the internet, or complex ecosystems can all be represented elegantly through mathematics. Because of the versatility of networks, determining how similar two networks are has wide application in the real world. By only analyzing the mathematical structure of two given networks, can we score their similarity to each other? Eventually we want to be able to classify an unknown network by scoring its similarity to, say, a social network, or a citation network, or a road network.
We are currently looking at ways to broaden node similarity algorithms to score networks as a whole. We have also extensively analyzed spectral measures. Future research includes complexity measures, centrality measures, and other inherent mathematical properties of networks.