Abstract by Mikelle Rogers
A Comparison of Effective Resistance and Katz Distance for Certain Families of Graphs
Effective Resistance and Katz Distance are two graphs metrics used for link prediction. Link prediction is used in many areas such as social media, online shopping, maps and the spreading of disease. Effective resistance is calculated by treating the graph as an electric circuit and then determining the resistance between nodes. The Katz distance considers the number of paths of different lengths between two nodes, weights these lengths and then sums them. When used for link prediction, both algorithms provide an ordered list of likely links. In this presentation, we will consider which values of the Katz constant give the same ordering of missing links as the effective resistance. Specifically, we will consider the range of the Katz constant for paths, cycles and linear two-trees (2-paths). The result of this work will allow mathematicians to know when to use which algorithm to predict links in a network based upon how the network’s links are formed.