Re: [igraph] (no subject)

[Tamas Nepusz]

Hi,

I think this is the same question as the one that you also posted on
Stack Overflow:

http://stackoverflow.com/questions/32878028/use-shortest-path-to-calculate-probability-of-connection

The answer is also posted there, but I'll summarize it here for the
list archives. Basically, you'll have to use the inverted logarithm of
the probabilities as edge weights in the shortest path calculations.

T.

T.


On Thu, Oct 1, 2015 at 2:43 AM, Ben Stewart-Koster
<address@hidden> wrote:
> Dear all,
>
> I'm wondering if there is a function within igraph way to calculate
> connection probabilities among vertices in a weighted graph, where the
> weights for the edges are probabilities of connection of the adjacent
> vertices.
>
> I've built a graph based on such an adjacency matrix where adjacent
> connection probabilities form the weights (this is for a river network so
> each node of the graph is only connected to a single downstream node).
>
> I had hoped to use something like the shortest paths function in igraph but
> that sums the weights rather than calculates the product of them and I can't
> work out a way to change that.
>
> I have included an example below where I construct the adjacency matrix from
> the data I have, which is the probability that the vertex is connected to
> the downstream vertex and then the identity of the downstream vertex.  The
> most downstream vertex is the river mouth so it is connected to no other
> (hence the downstream vector begins with NA).
>
> # vector of probability of connectivity to downstream node/vertice
>  ProbConn <- c(0, 1, 0.945881098491627, 0.997349787519144,
> 0.891475447373691,
> 0.993221681072185, 0.48071450525165, 0.0292543433507856, 0.0248645581575872,
> 1, 0.00540807765075205, 0.661465657844344, 0.108524549747512,
> 0.383311676351655, 0.708853495942148, 0.00150109592270933,
> 0.463859846404347,
> 0.0011491165581467, 2.87879700370202e-09, 0.536140153595653,
> 0.00831752330277812, 0.00185182893416988, 0.0186237313262708,
> 0.398961560996748, 0.582414707676981, 0.338534342155656, 1,
> 0.00137024127706289,
> 0.291146504057852, 1, 0.0743301054564134, 0.0514743607033332,
> 1, 1)
>
> # the downstream vertice of each node
> downstream <- c(NA, 1, 2, 3, 4, 5, 6, 2, 2, 7, 5, 8, 4, 6, 10, 3, 11, 3, 4,
> 11, 6, 6, 9, 9, 9, 8, 12, 5, 10, 13, 6, 6, 14, 15)
>
>  # Create the adjacency matrix from these vectors
>  adjacPI <- matrix(0, nrow=length(downstream), ncol=length(downstream)) #
> Set up the adjacency matrix to build the distance matrix
>
>
>         for (i in 1:length(downstream)) {
>                                     adjacPI[i, downstream[i]] <- ProbConn[i]
> # Fill the adjacency matrix
>                                     }
> # create the graph reflecting the downstream connectivity
>  PIgraph <- graph.adjacency(adjacPI, weighted=T)
> plot(PIgraph)
>
> PIpath <- shortest.paths(PIgraph, mode="out") # creates  the shortest paths
> matrix based on summing the distances of each step along each path
>                                               # Is it possible to calculate
> the product of the steps along each path?
>
>
> --
> Dr Ben Stewart-Koster
> Research Fellow
> Australian Rivers Institute
> Griffith University
> Ph: +61 7 3735 9206
> Fax: +61 7 3735 7615
>
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