Merge pull request #7 from JuliaGraphs/sbromberger/weighted-pagerank

weighted pagerank for SimpleWeightedDiGraph

Author: sbromberger

src/SimpleWeightedGraphs.jl

@@ -14,7 +14,8 @@ import LightGraphs:
 
     add_vertices!, adjacency_matrix, weights,
 
-    AbstractGraphFormat, loadgraph, loadgraphs, savegraph
+    AbstractGraphFormat, loadgraph, loadgraphs, savegraph,
+    pagerank
 
 export
     AbstractSimpleWeightedGraph,

src/overrides.jl

@@ -18,6 +18,41 @@ function adjacency_matrix(g::AbstractSimpleWeightedGraph, T::DataType=Int; dir::
     end
 end
 
+function pagerank(g::SimpleWeightedDiGraph, α=0.85, n=100::Integer, ϵ=1.0e-6)
+    A = weights(g)
+    S = vec(sum(A, 1))
+    S = 1 ./ S
+    S[find(S .== Inf)] = 0.0
+    M = A'  # need a separate line due to bug #17456 in julia
+    # scaling the adjmat to stochastic adjacency matrix
+    M = (Diagonal(S) * M)'
+    N = Int(nv(g))
+    # solution vector
+    x = fill(1.0 / N, N)
+    # personalization vector
+    p = fill(1.0 / N, N)
+    # temporary to hold the results of SpMV
+    y = zeros(Float64, N)
+    # adjustment for leaf nodes in digraph
+    dangling_weights = p
+    is_dangling = find(S .== 0)
+    # save some flops by precomputing this
+    pscaled = (1 .- α) .* p
+    for _ in 1:n
+        xlast = x
+        # in place SpMV to conserve memory
+        A_mul_B!(y, M, x)
+        # using broadcast to avoid temporaries
+        x = α .* (y .+ sum(x[is_dangling]) .* dangling_weights) .+ pscaled
+        # l1 change in solution convergence criterion
+        err = sum(abs, (x .- xlast))
+        if (err < N * ϵ)
+            return x
+        end
+    end
+    error("Pagerank did not converge after $n iterations.")
+end
+
 savegraph(fn::AbstractString, g::AbstractSimpleWeightedGraph, gname::AbstractString="graph"; compress=true) =
     savegraph(fn, g, gname, SWGFormat(), compress=compress)
 

test/overrides.jl

@@ -13,6 +13,10 @@
     for g in testdigraphs(g5)
         @test @inferred(adjacency_matrix(g, Bool)) == adjacency_matrix(g, Bool; dir=:out)
         @test adjacency_matrix(g; dir=:out) == adjacency_matrix(g; dir=:in)'
+        @test @inferred(pagerank(g))[3] ≈ 0.2266 atol=0.001
+        @test length(@inferred(pagerank(g))) == nv(g)
+        @test_throws ErrorException pagerank(g, 2)
+        @test_throws ErrorException pagerank(g, 0.85, 2)
     end
 end