// Farness returns the farness for nodes in the graph g used to construct
// the given shortest paths.
//
// F(v) = \sum_u d(u,v)
//
// For directed graphs the incoming paths are used. Infinite distances are
// not considered.
func Farness(g graph.Graph, p path.AllShortest) map[int]float64 {
nodes := g.Nodes()
f := make(map[int]float64, len(nodes))
for _, u := range nodes {
var sum float64
for _, v := range nodes {
// The ordering here is not relevant for
// undirected graphs, but we make sure we
// are counting incoming paths.
d := p.Weight(v, u)
if math.IsInf(d, 0) {
continue
}
sum += d
}
f[u.ID()] = sum
}
return f
}
// Harmonic returns the harmonic centrality for nodes in the graph g used to
// construct the given shortest paths.
//
// H(v)= \sum_{u ≠ v} 1 / d(u,v)
//
// For directed graphs the incoming paths are used. Infinite distances are
// not considered.
func Harmonic(g graph.Graph, p path.AllShortest) map[int]float64 {
nodes := g.Nodes()
h := make(map[int]float64, len(nodes))
for i, u := range nodes {
var sum float64
for j, v := range nodes {
// The ordering here is not relevant for
// undirected graphs, but we make sure we
// are counting incoming paths.
d := p.Weight(v, u)
if math.IsInf(d, 0) {
continue
}
if i != j {
sum += 1 / d
}
}
h[u.ID()] = sum
}
return h
}
// EdgeBetweennessWeighted returns the non-zero betweenness centrality for edges in
// the weighted graph g. For an edge e the centrality C_B is computed as
//
// C_B(e) = \sum_{s ≠ t ∈ V} (\sigma_{st}(e) / \sigma_{st}),
//
// where \sigma_{st} and \sigma_{st}(e) are the number of shortest paths from s
// to t, and the subset of those paths containing e, respectively.
//
// If g is undirected, edges are retained such that u.ID < v.ID where u and v are
// the nodes of e.
func EdgeBetweennessWeighted(g WeightedGraph, p path.AllShortest) map[[2]int]float64 {
cb := make(map[[2]int]float64)
_, isUndirected := g.(graph.Undirected)
nodes := g.Nodes()
for i, s := range nodes {
for j, t := range nodes {
if i == j {
continue
}
d := p.Weight(s, t)
if math.IsInf(d, 0) {
continue
}
// If we have a unique path, don't do the
// extra work needed to get all paths.
path, _, unique := p.Between(s, t)
if unique {
for k, v := range path[1:] {
// For undirected graphs we double count
// passage though edges. This is consistent
// with Brandes' algorithm's behaviour.
uid := path[k].ID()
vid := v.ID()
if isUndirected && vid < uid {
uid, vid = vid, uid
}
cb[[2]int{uid, vid}]++
}
continue
}
// Otherwise iterate over all paths.
paths, _ := p.AllBetween(s, t)
stFrac := 1 / float64(len(paths))
for _, path := range paths {
for k, v := range path[1:] {
uid := path[k].ID()
vid := v.ID()
if isUndirected && vid < uid {
uid, vid = vid, uid
}
cb[[2]int{uid, vid}] += stFrac
}
}
}
}
return cb
}
// BetweennessWeighted returns the non-zero betweenness centrality for nodes in the weighted
// graph g used to construct the given shortest paths.
//
// C_B(v) = \sum_{s ≠ v ≠ t ∈ V} (\sigma_{st}(v) / \sigma_{st})
//
// where \sigma_{st} and \sigma_{st}(v) are the number of shortest paths from s to t,
// and the subset of those paths containing v respectively.
func BetweennessWeighted(g WeightedGraph, p path.AllShortest) map[int]float64 {
cb := make(map[int]float64)
nodes := g.Nodes()
for i, s := range nodes {
for j, t := range nodes {
if i == j {
continue
}
d := p.Weight(s, t)
if math.IsInf(d, 0) {
continue
}
sID := s.ID()
tID := t.ID()
// If we have a unique path, don't do the
// extra work needed to get all paths.
path, _, unique := p.Between(s, t)
if unique {
for _, v := range path {
if vID := v.ID(); vID == sID || vID == tID {
continue
}
// For undirected graphs we double count
// passage though nodes. This is consistent
// with Brandes' algorithm's behaviour.
cb[v.ID()]++
}
continue
}
// Otherwise iterate over all paths.
paths, _ := p.AllBetween(s, t)
stFrac := 1 / float64(len(paths))
for _, path := range paths {
for _, v := range path {
if vID := v.ID(); vID == sID || vID == tID {
continue
}
cb[v.ID()] += stFrac
}
}
}
}
return cb
}
func TestDijkstraAllPaths(t *testing.T) {
for _, test := range shortestPathTests {
g := test.g()
for _, e := range test.edges {
g.SetEdge(e, e.Cost)
}
var (
pt path.AllShortest
panicked bool
)
func() {
defer func() {
panicked = recover() != nil
}()
pt = path.DijkstraAllPaths(g.(graph.Graph))
}()
if panicked || test.negative {
if !test.negative {
t.Errorf("%q: unexpected panic", test.name)
}
if !panicked {
t.Errorf("%q: expected panic for negative edge weight", test.name)
}
continue
}
// Check all random paths returned are OK.
for i := 0; i < 10; i++ {
p, weight, unique := pt.Between(test.query.From(), test.query.To())
if weight != test.weight {
t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
test.name, weight, test.weight)
}
if weight := pt.Weight(test.query.From(), test.query.To()); weight != test.weight {
t.Errorf("%q: unexpected weight from Weight: got:%f want:%f",
test.name, weight, test.weight)
}
if unique != test.unique {
t.Errorf("%q: unexpected number of paths: got: unique=%t want: unique=%t",
test.name, unique, test.unique)
}
var got []int
for _, n := range p {
got = append(got, n.ID())
}
ok := len(got) == 0 && len(test.want) == 0
for _, sp := range test.want {
if reflect.DeepEqual(got, sp) {
ok = true
break
}
}
if !ok {
t.Errorf("%q: unexpected shortest path:\ngot: %v\nwant from:%v",
test.name, p, test.want)
}
}
np, weight, unique := pt.Between(test.none.From(), test.none.To())
if np != nil || !math.IsInf(weight, 1) || unique != false {
t.Errorf("%q: unexpected path:\ngot: path=%v weight=%f unique=%t\nwant:path=<nil> weight=+Inf unique=false",
test.name, np, weight, unique)
}
paths, weight := pt.AllBetween(test.query.From(), test.query.To())
if weight != test.weight {
t.Errorf("%q: unexpected weight from Between: got:%f want:%f",
test.name, weight, test.weight)
}
var got [][]int
if len(paths) != 0 {
got = make([][]int, len(paths))
}
for i, p := range paths {
for _, v := range p {
got[i] = append(got[i], v.ID())
}
}
sort.Sort(internal.BySliceValues(got))
if !reflect.DeepEqual(got, test.want) {
t.Errorf("testing %q: unexpected shortest paths:\ngot: %v\nwant:%v",
test.name, got, test.want)
}
nps, weight := pt.AllBetween(test.none.From(), test.none.To())
if nps != nil || !math.IsInf(weight, 1) {
t.Errorf("%q: unexpected path:\ngot: paths=%v weight=%f\nwant:path=<nil> weight=+Inf",
test.name, nps, weight)
}
}
}