node2vec (Grover & Leskovec, 2016) introduces two hyperparameters to bias random walks. p (return): low p = likely to return to previous node (BFS — explores local neighborhood, captures homophily). q (in-out): low q = likely to go outward, high q = stay close (DFS vs BFS). The walk transition probability to node x from current v (came from t) is: 1/p if x=t, 1 if d(t,x)=1, 1/q if d(t,x)=2. The trail color shows BFS mode (warm) at low q vs DFS mode (cool) at high q — different structural roles are captured.