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Suppose we want to quantify the extent to which $v$ is between $s$ and $t$. There could be a few ways. One way to describe that extent is the probability of passing through $v$ if we want to reach from $s$ to $t$ by a randomly-selected shortest path. Assuming each shortest path is selected with equal probability, we will get $\frac{\sigma_{st}(v)}{\sigma_{... 3 However it doesn't seem to me that the formula calculates what is defined. The formula is right. The betweenness centrality is a value in an interval$[0, \ldots, 1]$. Thus, if the betweenness centrality of node$v$is equal to$1$, then all shortest paths between two nodes of this graph pass through$v$. I will explain the correctness of this summation ... 1 Certainly it is possible. For example, in the following study the Indian railway network was analyzed. Small-world properties of the Indian railway network. Parongama Sen, Subinay Dasgupta, Arnab Chatterjee, P. A. Sreeram, G. Mukherjee, and S. S. Manna. Phys. Rev. E 67, 036106 – 2003 In another study, the Chinese railway network was considered. W. Li, ... 1 Another heuristic idea: Find a long shortest path, and pick the vertex halfway along it. Pick a vertex and run BFS from it. For some small$k$, take the$k$furthest vertices from the original vertex that the BFS determines, and repeat the process on each of them, keeping the$k$overall furthest vertices each time. Repeat a few times. If the graph is a ... 1 After a bit of reading through literature I've come upon "closeness centrality" which is the reciprocal of what I'm calculating (mean distance, which they call "farness" in the article). But I still haven't found any algorithms for finding the "closeness center" (node with maximum closeness centrality) that is faster than$O(N^2)\$. As a heuristic, I have ...

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You're asking how to compute the shortest path between two vertices in a graph. Solution: use an algorithm for computing shortest paths. In your case, BFS would be a good choice. There's no need for A*.

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I don't know if there is a standard method to identify which activity matches which arrow, but I was able to complete your PERT chart by examining a few possible cases, while filling the chart from left to right. Each case was accepted or rejected after a while. I found that the higher arrow matches B and the lower C. Note that if you try to match C with the ...

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