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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package network
import (
"cmp"
"fmt"
"math"
"slices"
"testing"
"gonum.org/v1/gonum/floats/scalar"
"gonum.org/v1/gonum/graph/path"
"gonum.org/v1/gonum/graph/simple"
)
var betweennessTests = []struct {
g []set
wantTol float64
want map[int64]float64
wantEdges map[[2]int64]float64
}{
{
// Example graph from http://en.wikipedia.org/wiki/File:PageRanks-Example.svg 16:17, 8 July 2009
g: []set{
A: nil,
B: linksTo(C),
C: linksTo(B),
D: linksTo(A, B),
E: linksTo(D, B, F),
F: linksTo(B, E),
G: linksTo(B, E),
H: linksTo(B, E),
I: linksTo(B, E),
J: linksTo(E),
K: linksTo(E),
},
wantTol: 1e-1,
want: map[int64]float64{
B: 32,
D: 18,
E: 48,
},
wantEdges: map[[2]int64]float64{
{A, D}: 20,
{B, C}: 20,
{B, D}: 16,
{B, E}: 12,
{B, F}: 9,
{B, G}: 9,
{B, H}: 9,
{B, I}: 9,
{D, E}: 20,
{E, F}: 11,
{E, G}: 11,
{E, H}: 11,
{E, I}: 11,
{E, J}: 20,
{E, K}: 20,
},
},
{
// Example graph from http://en.wikipedia.org/w/index.php?title=PageRank&oldid=659286279#Power_Method
g: []set{
A: linksTo(B, C),
B: linksTo(D),
C: linksTo(D, E),
D: linksTo(E),
E: linksTo(A),
},
wantTol: 1e-3,
want: map[int64]float64{
A: 2,
B: 0.6667,
C: 0.6667,
D: 2,
E: 0.6667,
},
wantEdges: map[[2]int64]float64{
{A, B}: 2 + 2/3. + 4/2.,
{A, C}: 2 + 2/3. + 2/2.,
{A, E}: 2 + 2/3. + 2/2.,
{B, D}: 2 + 2/3. + 4/2.,
{C, D}: 2 + 2/3. + 2/2.,
{C, E}: 2,
{D, E}: 2 + 2/3. + 2/2.,
},
},
{
g: []set{
A: linksTo(B),
B: linksTo(C),
C: nil,
},
wantTol: 1e-3,
want: map[int64]float64{
B: 2,
},
wantEdges: map[[2]int64]float64{
{A, B}: 4,
{B, C}: 4,
},
},
{
g: []set{
A: linksTo(B),
B: linksTo(C),
C: linksTo(D),
D: linksTo(E),
E: nil,
},
wantTol: 1e-3,
want: map[int64]float64{
B: 6,
C: 8,
D: 6,
},
wantEdges: map[[2]int64]float64{
{A, B}: 8,
{B, C}: 12,
{C, D}: 12,
{D, E}: 8,
},
},
{
g: []set{
A: linksTo(C),
B: linksTo(C),
C: nil,
D: linksTo(C),
E: linksTo(C),
},
wantTol: 1e-3,
want: map[int64]float64{
C: 12,
},
wantEdges: map[[2]int64]float64{
{A, C}: 8,
{B, C}: 8,
{C, D}: 8,
{C, E}: 8,
},
},
{
g: []set{
A: linksTo(B, C, D, E),
B: linksTo(C, D, E),
C: linksTo(D, E),
D: linksTo(E),
E: nil,
},
wantTol: 1e-3,
want: map[int64]float64{},
wantEdges: map[[2]int64]float64{
{A, B}: 2,
{A, C}: 2,
{A, D}: 2,
{A, E}: 2,
{B, C}: 2,
{B, D}: 2,
{B, E}: 2,
{C, D}: 2,
{C, E}: 2,
{D, E}: 2,
},
},
}
func TestBetweenness(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewUndirectedGraph()
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if g.Node(int64(u)) == nil {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
got := Betweenness(g)
prec := 1 - int(math.Log10(test.wantTol))
for n := range test.g {
wantN, gotOK := got[int64(n)]
gotN, wantOK := test.want[int64(n)]
if gotOK != wantOK {
t.Errorf("unexpected betweenness result for test %d, node %c", i, n+'A')
}
if !scalar.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
i, orderedFloats(got, prec), orderedFloats(test.want, prec))
break
}
}
}
}
func TestEdgeBetweenness(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewUndirectedGraph()
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if g.Node(int64(u)) == nil {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
got := EdgeBetweenness(g)
prec := 1 - int(math.Log10(test.wantTol))
outer:
for u := range test.g {
for v := range test.g {
wantQ, gotOK := got[[2]int64{int64(u), int64(v)}]
gotQ, wantOK := test.wantEdges[[2]int64{int64(u), int64(v)}]
if gotOK != wantOK {
t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
}
if !scalar.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
break outer
}
}
}
}
}
func TestBetweennessWeighted(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if g.Node(int64(u)) == nil {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
p, ok := path.FloydWarshall(g)
if !ok {
t.Errorf("unexpected negative cycle in test %d", i)
continue
}
got := BetweennessWeighted(g, p)
prec := 1 - int(math.Log10(test.wantTol))
for n := range test.g {
gotN, gotOK := got[int64(n)]
wantN, wantOK := test.want[int64(n)]
if gotOK != wantOK {
t.Errorf("unexpected betweenness existence for test %d, node %c", i, n+'A')
}
if !scalar.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
i, orderedFloats(got, prec), orderedFloats(test.want, prec))
break
}
}
}
}
func TestEdgeBetweennessWeighted(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewWeightedUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if g.Node(int64(u)) == nil {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
p, ok := path.FloydWarshall(g)
if !ok {
t.Errorf("unexpected negative cycle in test %d", i)
continue
}
got := EdgeBetweennessWeighted(g, p)
prec := 1 - int(math.Log10(test.wantTol))
outer:
for u := range test.g {
for v := range test.g {
wantQ, gotOK := got[[2]int64{int64(u), int64(v)}]
gotQ, wantOK := test.wantEdges[[2]int64{int64(u), int64(v)}]
if gotOK != wantOK {
t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
}
if !scalar.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
break outer
}
}
}
}
}
func orderedPairFloats(w map[[2]int64]float64, prec int) []pairKeyFloatVal {
o := make([]pairKeyFloatVal, 0, len(w))
for k, v := range w {
o = append(o, pairKeyFloatVal{prec: prec, key: k, val: v})
}
slices.SortFunc(o, func(a, b pairKeyFloatVal) int {
if n := cmp.Compare(a.key[0], b.key[0]); n != 0 {
return n
}
return cmp.Compare(a.key[1], b.key[1])
})
return o
}
type pairKeyFloatVal struct {
prec int
key [2]int64
val float64
}
func (kv pairKeyFloatVal) String() string {
return fmt.Sprintf("(%c,%c):%.*f", kv.key[0]+'A', kv.key[1]+'A', kv.prec, kv.val)
}
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