node2vec

The problem, from first principles

node2vec extends DeepWalk with biased random walks controlled by return parameter p and in-out parameter q. These parameters control exploration depth vs. breadth.

High p: discourage immediate returns to previous node. High q: breadth-first exploration.

From theory to code

Implement:

biased_random_walk(adj, start_node, walk_length, p, q)

Constraints

• adj shape: (num_nodes, num_nodes).
• start_node, walk_length: int.
• p, q: positive floats (transition probabilities).
• Return shape: (walk_length,).