Metrics to Consider

1. Similarity of nodes, specifically structural equivalence and cosine similarity
   • Cosine Similarity: measure of structural equivalence on undirected networks
     • Need a way to normalize count of common neighbors across graph: Pearson coefficient (compare to expected value in random network)
     • Pearson Correlation Coefficient : $r_{ij} = \frac{Cov(X_i, X_j)}{\sqrt{Var(X_i)Var(X_j)}}$ where $X_i$ is the indicator random variable that a randomly chosen node is the neighbor of node $i$.
   • Direct Application: Measure of similarity that takes into account structural equivalence as well as similar properties/characteristics, that all evolves over time
     • What marriages are similar to X?
     • What marriages show a similar trend over time to X?