random walk with restart (dgl 0.4.3 version)

[atesnrllh]

I understood that "restart_prob" effect random walk length and "max_nodes_per_seed" effect trace numbers. I tested "random_walk_with_restart" with many different parameters. I notice that "restart_prob" effect trace number also. But I dont understand how "restart_prob" effect trace number? Now I am using dgl new version and I should understand this old function to code it with new dgl library.

[BarclayII]

What do you mean by "trace number"?

[atesnrllh]

In the old version a "max_nodes_per_seed" parameter gives the maximum number of traces. But the number of traces is variable. That's why I thought the number of traces depends on the "restart_prob" parameter. Because when this parameter gets bigger, the total number of traces also increases, and when it gets smaller, the total number of traces also decreases. Actually, the "restart_prob" parameter determines the length of the random walk. I know this. But I am not sure if it affects the total trace count. If it does, how does it affect it?

dgl 0.4.3 random_walk_with_restart function

**def random_walk_with_restart( g, seeds, restart_prob, max_nodes_per_seed, max_visit_counts=0, max_frequent_visited_nodes=0): """Batch-generate random walk traces on given graph with restart probability.

Parameters
----------
g : DGLGraph
    The graph.
seeds : Tensor
    The node ID tensor from which the random walk traces starts.
restart_prob : float
    Probability to stop a random walk after each step.
max_nodes_per_seed : int
    Stop generating traces for a seed if the total number of nodes
    visited exceeds this number. [1]
max_visit_counts : int, optional
max_frequent_visited_nodes : int, optional
    Alternatively, stop generating traces for a seed if no less than
    ``max_frequent_visited_nodes`` are visited no less than
    ``max_visit_counts`` times.  [1]**

[BarclayII]

It shouldn't affect the number of random walk paths. That should be always equal to the number of seeds.

[atesnrllh]

Everything is the same except restart_prob. I tested "0.4.3 dgl random_walk_with_restart" function with different restart_prob. I run it 10 times with for loop.

walks = dgl.contrib.sampling.random_walk_with_restart(G, seeds=[1], restart_prob=0.9,max_nodes_per_seed=256)

Total number of traces for 10 for loops: 2293

walks = dgl.contrib.sampling.random_walk_with_restart(G, seeds=[1], restart_prob=0.5,max_nodes_per_seed=256)

Total number of traces for 10 for loops: 1307

walks = dgl.contrib.sampling.random_walk_with_restart(G, seeds=[1], restart_prob=0.1,max_nodes_per_seed=256)

Total number of traces for 10 for loops: : 237

[BarclayII]

We have stopped supporting 0.4.3. Could you check out this function that also has restart probability support?

[github-actions[bot]]

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