Lecture 9: Measures and Metrics

Transitivity is way of deriving path between two nodes using existent paths. Sure, there is a rule for this derivation. Rule can be visualized as follows: There exist 3 nodes A,B and C in our network. If there exists path from A to B and B to C , then we can conclude that path from A to C also exists.

Clustering coefficient can be defined as

c= (# of triangles x 3)/# of connected triples

For a clique(every node is connected to each other) , c equals 1. Clustering coefficient is used to understand network's structure such that if c is greater than 0.001 (this is an approximate number) that network can be defined as dense network.

For a node in network, complexity coefficient can also be calculated using following formula

C(i)= (#of neighbors of i that are connected)/(#of pairs of neighbors of i)

Reciprocity in networks is defined as mutual edges between two nodes. That is, if there exists directed edge from node A to Node B, then edge from node B to node A must exist.

Similarity is another issue between nodes in network that we mentioned. There are 3 types of similarity.

1. Equal Similarity: Nodes have exactly same neighbors.
2. Structural Similarity: Nodes have many common neighbors. Used for measuring nodes' structural closing. Cosine similarity is used to calculate.
3. Regular Equivalence: Nodes have different nodes, however structure of neighbors are similar.

There are also other theorems that measure similarity using different parameters such as Euclidean Similarity and Pearson Similarity