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// Copyright ©2016 The Gonum Authors. All rights reserved.
// Copyright 2021 The Go Authors. All rights reserved.
// (above line required for our license-header checker)
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package community_test
import (
"fmt"
"log"
"sort"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/graph/community"
"gonum.org/v1/gonum/graph/internal/ordered"
"gonum.org/v1/gonum/graph/simple"
)
func ExampleProfile_simple() {
// Profile calls Modularize which implements the Louvain modularization algorithm.
// Since this is a randomized algorithm we use a defined random source to ensure
// consistency between test runs. In practice, results will not differ greatly
// between runs with different PRNG seeds.
src := rand.NewSource(1)
// Create dumbell graph:
//
// 0 4
// |\ /|
// | 2 - 3 |
// |/ \|
// 1 5
//
g := simple.NewUndirectedGraph()
for u, e := range smallDumbell {
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
// Get the profile of internal node weight for resolutions
// between 0.1 and 10 using logarithmic bisection.
p, err := community.Profile(
community.ModularScore(g, community.Weight, 10, src),
true, 1e-3, 0.1, 10,
)
if err != nil {
log.Fatal(err)
}
// Print out each step with communities ordered.
for _, d := range p {
comm := d.Communities()
for _, c := range comm {
sort.Sort(ordered.ByID(c))
}
sort.Sort(ordered.BySliceIDs(comm))
fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
d.Low, d.High, d.Score, comm, community.Q(g, comm, d.Low))
}
// Output:
// Low:0.1 High:0.29 Score:14 Communities:[[0 1 2 3 4 5]] Q=0.9
// Low:0.29 High:2.3 Score:12 Communities:[[0 1 2] [3 4 5]] Q=0.714
// Low:2.3 High:3.5 Score:4 Communities:[[0 1] [2] [3] [4 5]] Q=-0.31
// Low:3.5 High:10 Score:0 Communities:[[0] [1] [2] [3] [4] [5]] Q=-0.607
}
// intset is an integer set.
type intset map[int]struct{}
func linksTo(i ...int) intset {
if len(i) == 0 {
return nil
}
s := make(intset)
for _, v := range i {
s[v] = struct{}{}
}
return s
}
var (
smallDumbell = []intset{
0: linksTo(1, 2),
1: linksTo(2),
2: linksTo(3),
3: linksTo(4, 5),
4: linksTo(5),
5: nil,
}
// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
middleEast = struct{ friends, complicated, enemies []intset }{
// green cells
friends: []intset{
0: nil,
1: linksTo(5, 7, 9, 12),
2: linksTo(11),
3: linksTo(4, 5, 10),
4: linksTo(3, 5, 10),
5: linksTo(1, 3, 4, 8, 10, 12),
6: nil,
7: linksTo(1, 12),
8: linksTo(5, 9, 11),
9: linksTo(1, 8, 12),
10: linksTo(3, 4, 5),
11: linksTo(2, 8),
12: linksTo(1, 5, 7, 9),
},
// yellow cells
complicated: []intset{
0: linksTo(2, 4),
1: linksTo(4, 8),
2: linksTo(0, 3, 4, 5, 8, 9),
3: linksTo(2, 8, 11),
4: linksTo(0, 1, 2, 8),
5: linksTo(2),
6: nil,
7: linksTo(9, 11),
8: linksTo(1, 2, 3, 4, 10, 12),
9: linksTo(2, 7, 11),
10: linksTo(8),
11: linksTo(3, 7, 9, 12),
12: linksTo(8, 11),
},
// red cells
enemies: []intset{
0: linksTo(1, 3, 5, 6, 7, 8, 9, 10, 11, 12),
1: linksTo(0, 2, 3, 6, 10, 11),
2: linksTo(1, 6, 7, 10, 12),
3: linksTo(0, 1, 6, 7, 9, 12),
4: linksTo(6, 7, 9, 11, 12),
5: linksTo(0, 6, 7, 9, 11),
6: linksTo(0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12),
7: linksTo(0, 2, 3, 4, 5, 6, 8, 10),
8: linksTo(0, 6, 7),
9: linksTo(0, 3, 4, 5, 6, 10),
10: linksTo(0, 1, 2, 6, 7, 9, 11, 12),
11: linksTo(0, 1, 4, 5, 6, 10),
12: linksTo(0, 2, 3, 4, 6, 10),
},
}
)
var friends, enemies *simple.WeightedUndirectedGraph
func init() {
friends = simple.NewWeightedUndirectedGraph(0, 0)
for u, e := range middleEast.friends {
// Ensure unconnected nodes are included.
if friends.Node(int64(u)) == nil {
friends.AddNode(simple.Node(u))
}
for v := range e {
friends.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
enemies = simple.NewWeightedUndirectedGraph(0, 0)
for u, e := range middleEast.enemies {
// Ensure unconnected nodes are included.
if enemies.Node(int64(u)) == nil {
enemies.AddNode(simple.Node(u))
}
for v := range e {
enemies.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: -1})
}
}
}
func ExampleProfile_multiplex() {
// Profile calls ModularizeMultiplex which implements the Louvain modularization
// algorithm. Since this is a randomized algorithm we use a defined random source
// to ensure consistency between test runs. In practice, results will not differ
// greatly between runs with different PRNG seeds.
src := rand.NewSource(1)
// The undirected graphs, friends and enemies, are the political relationships
// in the Middle East as described in the Slate article:
// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
g, err := community.NewUndirectedLayers(friends, enemies)
if err != nil {
log.Fatal(err)
}
weights := []float64{1, -1}
// Get the profile of internal node weight for resolutions
// between 0.1 and 10 using logarithmic bisection.
p, err := community.Profile(
community.ModularMultiplexScore(g, weights, true, community.WeightMultiplex, 10, src),
true, 1e-3, 0.1, 10,
)
if err != nil {
log.Fatal(err)
}
// Print out each step with communities ordered.
for _, d := range p {
comm := d.Communities()
for _, c := range comm {
sort.Sort(ordered.ByID(c))
}
sort.Sort(ordered.BySliceIDs(comm))
fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
d.Low, d.High, d.Score, comm, community.QMultiplex(g, comm, weights, []float64{d.Low}))
}
// Output:
// Low:0.1 High:0.72 Score:26 Communities:[[0] [1 7 9 12] [2 8 11] [3 4 5 10] [6]] Q=[24.7 1.97]
// Low:0.72 High:1.1 Score:24 Communities:[[0 6] [1 7 9 12] [2 8 11] [3 4 5 10]] Q=[16.9 14.1]
// Low:1.1 High:1.2 Score:18 Communities:[[0 2 6 11] [1 7 9 12] [3 4 5 8 10]] Q=[9.16 25.1]
// Low:1.2 High:1.6 Score:10 Communities:[[0 3 4 5 6 10] [1 7 9 12] [2 8 11]] Q=[10.5 26.7]
// Low:1.6 High:1.6 Score:8 Communities:[[0 1 6 7 9 12] [2 8 11] [3 4 5 10]] Q=[5.56 39.8]
// Low:1.6 High:1.8 Score:2 Communities:[[0 2 3 4 5 6 10] [1 7 8 9 11 12]] Q=[-1.82 48.6]
// Low:1.8 High:2.3 Score:-6 Communities:[[0 2 3 4 5 6 8 10 11] [1 7 9 12]] Q=[-5 57.5]
// Low:2.3 High:2.4 Score:-10 Communities:[[0 1 2 6 7 8 9 11 12] [3 4 5 10]] Q=[-11.2 79]
// Low:2.4 High:4.3 Score:-52 Communities:[[0 1 2 3 4 5 6 7 8 9 10 11 12]] Q=[-46.1 117]
// Low:4.3 High:10 Score:-54 Communities:[[0 1 2 3 4 6 7 8 9 10 11 12] [5]] Q=[-82 254]
}
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