Implement laplacian_lambda_max (#240)

* Add laplacian_lambda_max function

* Add laplacian_lambda_max tests

* Add export laplacian_lambda_max

* Fix style

* Fix docstring

Co-authored-by: Carlo Lucibello <[email protected]>

* Fix indentation

Co-authored-by: Carlo Lucibello <[email protected]>

* Add spaces

Co-authored-by: Carlo Lucibello <[email protected]>

Add spaces

Co-authored-by: Carlo Lucibello <[email protected]>

Add spaces

Co-authored-by: Carlo Lucibello <[email protected]>

Add spaces

Co-authored-by: Carlo Lucibello <[email protected]>

Add spaces

Co-authored-by: Carlo Lucibello <[email protected]>

Co-authored-by: Carlo Lucibello <[email protected]>

Author: aurorarossi

src/GNNGraphs/GNNGraphs.jl

@@ -35,6 +35,7 @@ export adjacency_list,
        is_bidirected,
        normalized_laplacian, 
        scaled_laplacian,
+       laplacian_lambda_max,
        # from Graphs
        adjacency_matrix, 
        degree, 

src/GNNGraphs/query.jl

@@ -414,6 +414,25 @@ function khop_adj(g::GNNGraph,k::Int, T::DataType=eltype(g); dir=:out, weighted=
     return (adjacency_matrix(g, T; dir, weighted))^k
 end
 
+"""
+    laplacian_lambda_max(g::GNNGraph, T=Float32; add_self_loops=false, dir=:out)
+
+Return the largest eigenvalue of the normalized symmetric Laplacian of the graph `g`.
+
+If the graph is batched from multiple graphs, return the list of the largest eigenvalue for each graph.
+"""
+function laplacian_lambda_max(g::GNNGraph,T::DataType=Float32; 
+                             add_self_loops::Bool=false, dir::Symbol=:out)
+    if g.num_graphs==1
+        return _eigmax(normalized_laplacian(g, T; add_self_loops, dir))
+    else
+        eigenvalues=zeros(g.num_graphs)
+        for i in 1:g.num_graphs
+            eigenvalues[i] = _eigmax(normalized_laplacian(getgraph(g, i), T; add_self_loops, dir))
+        end
+        return eigenvalues
+    end
+end
 
 @non_differentiable edge_index(x...)
 @non_differentiable adjacency_list(x...)

test/GNNGraphs/query.jl

@@ -132,6 +132,19 @@
         @test L ≈ D - A
     end
 
+    @testset "laplacian_lambda_max" begin
+        s = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]
+        t = [2, 3, 4, 5, 1, 5, 1, 2, 3, 4]
+        g = GNNGraph(s,t)
+        @test laplacian_lambda_max(g) ≈ Float32(1.809017)
+        data1 = [g for i in 1:5]
+        gall1 = Flux.batch(data1)
+        @test laplacian_lambda_max(gall1) ≈ [Float32(1.809017) for i in 1:5]
+        data2 = [rand_graph(10,20) for i in 1:3]
+        gall2 = Flux.batch(data2)
+        @test length(laplacian_lambda_max(gall2)) == 3
+    end
+
     @testset "adjacency_matrix" begin
         a = sprand(5, 5, 0.5)
         abin = map(x -> x > 0 ? 1 : 0, a)