Example #1
0
// 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
}
Example #2
0
// 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
}
Example #3
0
// 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
}
Example #4
0
// 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
}
Example #5
0
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)
		}
	}
}