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