Jaccard similarity:

measures similarity between sample sets -

\[J(a, b) = \frac{A \cap B}{A \cup B}\]

Problem with previous similarity functions

You need to re-run the algorithm again when new node has been added.

Graph Neural Network

learn the mapping between node and vector.

Train the model

Directly train the model for a supervised task (e.g., node classification)

• After K-layers of neighborhood aggregation, we get output embeddings for each node.

• We can feed these embeddings into any loss function and run stochastic gradient descent to train the aggregation parameters. 

Granovetter's explaination

Define Bridge edge

• If removed, it disconnects the graph
• Extremely rare in social networks

Define: Local bridge

• Endpoints have no friends in common

• a Edge of Span > 2 (Span of an edge is the distance of the edge endpoints if the edge is deleted. Local bridges with long span are like real bridges)

Define: Two types of edges:

• Strong (friend), Weak (acquaintance) Define: Strong triadic closure:

• Two strong ties imply a third edge