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220 lines
6.4 KiB
Go
220 lines
6.4 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package community_test
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import (
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"fmt"
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"log"
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"math/rand/v2"
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"gonum.org/v1/gonum/graph/community"
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"gonum.org/v1/gonum/graph/simple"
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"gonum.org/v1/gonum/internal/order"
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)
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func ExampleProfile_simple() {
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// Profile calls Modularize which implements the Louvain modularization algorithm.
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// Since this is a randomized algorithm we use a defined random source to ensure
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// consistency between test runs. In practice, results will not differ greatly
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// between runs with different PRNG seeds.
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src := rand.NewPCG(1, 1)
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// Create dumbell graph:
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//
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// 0 4
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// |\ /|
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// | 2 - 3 |
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// |/ \|
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// 1 5
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//
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g := simple.NewUndirectedGraph()
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for u, e := range smallDumbell {
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for v := range e {
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g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
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}
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}
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// Get the profile of internal node weight for resolutions
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// between 0.1 and 10 using logarithmic bisection.
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p, err := community.Profile(
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community.ModularScore(g, community.Weight, 10, src),
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true, 1e-3, 0.1, 10,
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)
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if err != nil {
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log.Fatal(err)
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}
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// Print out each step with communities ordered.
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for _, d := range p {
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comm := d.Communities()
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for _, c := range comm {
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order.ByID(c)
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}
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order.BySliceIDs(comm)
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fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
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d.Low, d.High, d.Score, comm, community.Q(g, comm, d.Low))
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}
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// Output:
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// Low:0.1 High:0.29 Score:14 Communities:[[0 1 2 3 4 5]] Q=0.9
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// Low:0.29 High:2.3 Score:12 Communities:[[0 1 2] [3 4 5]] Q=0.714
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// Low:2.3 High:3.5 Score:4 Communities:[[0 1] [2] [3] [4 5]] Q=-0.31
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// Low:3.5 High:10 Score:0 Communities:[[0] [1] [2] [3] [4] [5]] Q=-0.607
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}
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// intset is an integer set.
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type intset map[int]struct{}
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func linksTo(i ...int) intset {
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if len(i) == 0 {
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return nil
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}
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s := make(intset)
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for _, v := range i {
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s[v] = struct{}{}
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}
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return s
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}
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var (
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smallDumbell = []intset{
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0: linksTo(1, 2),
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1: linksTo(2),
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2: linksTo(3),
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3: linksTo(4, 5),
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4: linksTo(5),
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5: nil,
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}
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// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
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middleEast = struct{ friends, complicated, enemies []intset }{
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// green cells
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friends: []intset{
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0: nil,
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1: linksTo(5, 7, 9, 12),
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2: linksTo(11),
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3: linksTo(4, 5, 10),
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4: linksTo(3, 5, 10),
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5: linksTo(1, 3, 4, 8, 10, 12),
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6: nil,
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7: linksTo(1, 12),
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8: linksTo(5, 9, 11),
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9: linksTo(1, 8, 12),
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10: linksTo(3, 4, 5),
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11: linksTo(2, 8),
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12: linksTo(1, 5, 7, 9),
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},
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// yellow cells
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complicated: []intset{
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0: linksTo(2, 4),
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1: linksTo(4, 8),
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2: linksTo(0, 3, 4, 5, 8, 9),
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3: linksTo(2, 8, 11),
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4: linksTo(0, 1, 2, 8),
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5: linksTo(2),
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6: nil,
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7: linksTo(9, 11),
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8: linksTo(1, 2, 3, 4, 10, 12),
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9: linksTo(2, 7, 11),
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10: linksTo(8),
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11: linksTo(3, 7, 9, 12),
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12: linksTo(8, 11),
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},
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// red cells
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enemies: []intset{
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0: linksTo(1, 3, 5, 6, 7, 8, 9, 10, 11, 12),
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1: linksTo(0, 2, 3, 6, 10, 11),
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2: linksTo(1, 6, 7, 10, 12),
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3: linksTo(0, 1, 6, 7, 9, 12),
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4: linksTo(6, 7, 9, 11, 12),
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5: linksTo(0, 6, 7, 9, 11),
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6: linksTo(0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12),
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7: linksTo(0, 2, 3, 4, 5, 6, 8, 10),
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8: linksTo(0, 6, 7),
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9: linksTo(0, 3, 4, 5, 6, 10),
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10: linksTo(0, 1, 2, 6, 7, 9, 11, 12),
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11: linksTo(0, 1, 4, 5, 6, 10),
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12: linksTo(0, 2, 3, 4, 6, 10),
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},
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}
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)
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var friends, enemies *simple.WeightedUndirectedGraph
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func init() {
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friends = simple.NewWeightedUndirectedGraph(0, 0)
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for u, e := range middleEast.friends {
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// Ensure unconnected nodes are included.
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if friends.Node(int64(u)) == nil {
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friends.AddNode(simple.Node(u))
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}
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for v := range e {
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friends.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
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}
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}
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enemies = simple.NewWeightedUndirectedGraph(0, 0)
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for u, e := range middleEast.enemies {
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// Ensure unconnected nodes are included.
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if enemies.Node(int64(u)) == nil {
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enemies.AddNode(simple.Node(u))
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}
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for v := range e {
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enemies.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: -1})
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}
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}
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}
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func ExampleProfile_multiplex() {
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// Profile calls ModularizeMultiplex which implements the Louvain modularization
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// algorithm. Since this is a randomized algorithm we use a defined random source
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// to ensure consistency between test runs. In practice, results will not differ
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// greatly between runs with different PRNG seeds.
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src := rand.NewPCG(1, 1)
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// The undirected graphs, friends and enemies, are the political relationships
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// in the Middle East as described in the Slate article:
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// http://www.slate.com/blogs/the_world_/2014/07/17/the_middle_east_friendship_chart.html
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g, err := community.NewUndirectedLayers(friends, enemies)
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if err != nil {
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log.Fatal(err)
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}
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weights := []float64{1, -1}
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// Get the profile of internal node weight for resolutions
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// between 0.1 and 10 using logarithmic bisection.
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p, err := community.Profile(
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community.ModularMultiplexScore(g, weights, true, community.WeightMultiplex, 10, src),
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true, 1e-3, 0.1, 10,
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)
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if err != nil {
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log.Fatal(err)
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}
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// Print out each step with communities ordered.
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for _, d := range p {
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comm := d.Communities()
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for _, c := range comm {
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order.ByID(c)
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}
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order.BySliceIDs(comm)
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fmt.Printf("Low:%.2v High:%.2v Score:%v Communities:%v Q=%.3v\n",
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d.Low, d.High, d.Score, comm, community.QMultiplex(g, comm, weights, []float64{d.Low}))
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}
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// Output:
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// 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]
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// 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]
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// 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]
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// Low:1.2 High:1.6 Score:10 Communities:[[0 3 4 5 6 10] [1 7 9 12] [2 8 11]] Q=[10.7 26]
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// 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]
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// 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]
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// Low:1.8 High:2.3 Score:-6 Communities:[[0 2 3 4 5 6 8 10 11] [1 7 9 12]] Q=[-5.02 57.5]
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// 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]
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// 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]
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// 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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}
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