Is there a way to normalize paths to calculate node importance in a random walk undirected graph?

Question

We constructed a graph and conducted n=100 random walks from a source node to a sink node. The edges in the graph are weighted to reflect the associations between the nodes. Our objective is to assess the proximity of each node to the sink node in these random walks. Initially, we considered a simple approach of normalizing each node's position based on the length of the walk. For instance, if a path goes from an initial source node to node A, then to node B, and finally to the sink node with a total path length of 4, node A would be assigned a value of 2/4, and node B would be assigned 3/4, and the sink would be 1. Is there a better way to do this (i.e. via some sort of centrality/closeness normalization method)? We want to calculate node importance values ultimately.

we have yet to implement this in our code.

Answer 1

objective is to assess the proximity of each node to the sink node in these random walks.

Loop over the nodes, except 'sink'
   Find shortest path from sink to node ( breadth first search )
   Assign reciprocal of path length as node "importance"