// edgeNodesFor returns the pair of nodes for the ith edge in a simple
// undirected graph. The pair is returned such that w.ID < v.ID.
func edgeNodesFor(i int) (v, w simple.Node) {
// This is an algebraic simplification of the expressions described
// on p3 of http://algo.uni-konstanz.de/publications/bb-eglrn-05.pdf
v = simple.Node(0.5 + math.Sqrt(float64(1+8*i))/2)
w = simple.Node(i) - v*(v-1)/2
return v, w
}
// Builds a BFS tree (as a directed graph) from the given graph and start node.
func BFSTree(g graph.Graph, start graph.Node) *simple.DirectedGraph {
if !g.Has(start) {
panic(fmt.Sprintf("BFSTree: Start node %r not in graph %r", start, g))
}
ret := simple.NewDirectedGraph(0.0, math.Inf(1))
seen := make(map[int]bool)
q := queue.New()
q.Add(start)
ret.AddNode(simple.Node(start.ID()))
for q.Length() > 0 {
node := q.Peek().(graph.Node)
q.Remove()
for _, neighbor := range g.From(node) {
if !seen[neighbor.ID()] {
seen[neighbor.ID()] = true
ret.AddNode(simple.Node(neighbor.ID()))
ret.SetEdge(simple.Edge{F: simple.Node(node.ID()), T: simple.Node(neighbor.ID()), W: g.Edge(node, neighbor).Weight()})
q.Add(neighbor)
}
}
}
return ret
}
func TestCommunityQ(t *testing.T) {
for _, test := range communityQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
}
got := Q(g, communities, structure.resolution)
if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && math.IsNaN(got) != math.IsNaN(structure.want) {
for _, c := range communities {
sort.Sort(ordered.ByID(c))
}
t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
test.name, communities, got, structure.want)
}
}
}
}
func TestBetweennessWeighted(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{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[n]
wantN, wantOK := test.want[n]
if gotOK != wantOK {
t.Errorf("unexpected betweenness existence for test %d, node %c", i, n+'A')
}
if !floats.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 TestDepthFirst(t *testing.T) {
for i, test := range depthFirstTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
w := DepthFirst{
EdgeFilter: test.edge,
}
var got []int
final := w.Walk(g, test.from, func(n graph.Node) bool {
if test.until != nil && test.until(n) {
return true
}
got = append(got, n.ID())
return false
})
if !test.final[final] {
t.Errorf("unexepected final node for test %d:\ngot: %v\nwant: %v", i, final, test.final)
}
sort.Ints(got)
if test.want != nil && !reflect.DeepEqual(got, test.want) {
t.Errorf("unexepected DFS traversed nodes for test %d:\ngot: %v\nwant: %v", i, got, test.want)
}
}
}
func TestHITS(t *testing.T) {
for i, test := range hitsTests {
g := simple.NewDirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
got := HITS(g, test.tol)
prec := 1 - int(math.Log10(test.wantTol))
for n := range test.g {
if !floats.EqualWithinAbsOrRel(got[n].Hub, test.want[n].Hub, test.wantTol, test.wantTol) {
t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
break
}
if !floats.EqualWithinAbsOrRel(got[n].Authority, test.want[n].Authority, test.wantTol, test.wantTol) {
t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
break
}
}
}
}
func TestSort(t *testing.T) {
for i, test := range tarjanTests {
g := simple.NewDirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
sorted, err := Sort(g)
var gotSortedLen int
for _, n := range sorted {
if n != nil {
gotSortedLen++
}
}
if gotSortedLen != test.sortedLength {
t.Errorf("unexpected number of sortable nodes for test %d: got:%d want:%d", i, gotSortedLen, test.sortedLength)
}
if err == nil != test.sortable {
t.Errorf("unexpected sortability for test %d: got error: %v want: nil-error=%t", i, err, test.sortable)
}
if err != nil && len(err.(Unorderable)) != test.unorderableLength {
t.Errorf("unexpected number of unorderable nodes for test %d: got:%d want:%d", i, len(err.(Unorderable)), test.unorderableLength)
}
}
}
func TestTarjanSCC(t *testing.T) {
for i, test := range tarjanTests {
g := simple.NewDirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
gotSCCs := TarjanSCC(g)
// tarjan.strongconnect does range iteration over maps,
// so sort SCC members to ensure consistent ordering.
gotIDs := make([][]int, len(gotSCCs))
for i, scc := range gotSCCs {
gotIDs[i] = make([]int, len(scc))
for j, id := range scc {
gotIDs[i][j] = id.ID()
}
sort.Ints(gotIDs[i])
}
for _, iv := range test.ambiguousOrder {
sort.Sort(internal.BySliceValues(test.want[iv.start:iv.end]))
sort.Sort(internal.BySliceValues(gotIDs[iv.start:iv.end]))
}
if !reflect.DeepEqual(gotIDs, test.want) {
t.Errorf("unexpected Tarjan scc result for %d:\n\tgot:%v\n\twant:%v", i, gotIDs, test.want)
}
}
}
func TestAStar(t *testing.T) {
for _, test := range aStarTests {
pt, _ := AStar(simple.Node(test.s), simple.Node(test.t), test.g, test.heuristic)
p, cost := pt.To(simple.Node(test.t))
if !topo.IsPathIn(test.g, p) {
t.Error("got path that is not path in input graph for %q", test.name)
}
bfp, ok := BellmanFordFrom(simple.Node(test.s), test.g)
if !ok {
t.Fatalf("unexpected negative cycle in %q", test.name)
}
if want := bfp.WeightTo(simple.Node(test.t)); cost != want {
t.Errorf("unexpected cost for %q: got:%v want:%v", test.name, cost, want)
}
var got = make([]int, 0, len(p))
for _, n := range p {
got = append(got, n.ID())
}
if test.wantPath != nil && !reflect.DeepEqual(got, test.wantPath) {
t.Errorf("unexpected result for %q:\ngot: %v\nwant:%v", test.name, got, test.wantPath)
}
}
}
func TestBronKerbosch(t *testing.T) {
for i, test := range bronKerboschTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
cliques := BronKerbosch(g)
got := make([][]int, len(cliques))
for j, c := range cliques {
ids := make([]int, len(c))
for k, n := range c {
ids[k] = n.ID()
}
sort.Ints(ids)
got[j] = ids
}
sort.Sort(ordered.BySliceValues(got))
if !reflect.DeepEqual(got, test.want) {
t.Errorf("unexpected cliques for test %d:\ngot: %v\nwant:%v", i, got, test.want)
}
}
}
func TestCyclesIn(t *testing.T) {
for i, test := range cyclesInTests {
g := simple.NewDirectedGraph(0, math.Inf(1))
g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
cycles := CyclesIn(g)
var got [][]int
if cycles != nil {
got = make([][]int, len(cycles))
}
// johnson.circuit does range iteration over maps,
// so sort to ensure consistent ordering.
for j, c := range cycles {
ids := make([]int, len(c))
for k, n := range c {
ids[k] = n.ID()
}
got[j] = ids
}
sort.Sort(ordered.BySliceValues(got))
if !reflect.DeepEqual(got, test.want) {
t.Errorf("unexpected johnson result for %d:\n\tgot:%#v\n\twant:%#v", i, got, test.want)
}
}
}
func TestEdgeBetweenness(t *testing.T) {
for i, test := range betweennessTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
// Weight omitted to show weight-independence.
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 0})
}
}
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]int{u, v}]
gotQ, wantOK := test.wantEdges[[2]int{u, v}]
if gotOK != wantOK {
t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
}
if !floats.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
}
}
}
}
}
// Gnm constructs a graph in the destination, dst, of order n and size m. If src is not
// nil it is used as the random source, otherwise rand.Float64 is used. The graph is
// constructed in O(m) expected time for m ≤ (n choose 2)/2.
func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
if m == 0 {
return nil
}
hasEdge := dst.HasEdgeBetween
d, isDirected := dst.(graph.Directed)
if isDirected {
m /= 2
hasEdge = d.HasEdgeFromTo
}
nChoose2 := (n - 1) * n / 2
if m < 0 || m > nChoose2 {
return fmt.Errorf("gen: bad size: m=%d", m)
}
var rnd func(int) int
if src == nil {
rnd = rand.Intn
} else {
rnd = src.Intn
}
for i := 0; i < n; i++ {
if !dst.Has(simple.Node(i)) {
dst.AddNode(simple.Node(i))
}
}
// Add forward edges for all graphs.
for i := 0; i < m; i++ {
for {
v, w := edgeNodesFor(rnd(nChoose2))
e := simple.Edge{F: w, T: v, W: 1}
if !hasEdge(e.F, e.T) {
dst.SetEdge(e)
break
}
}
}
// Add backward edges for directed graphs.
if !isDirected {
return nil
}
for i := 0; i < m; i++ {
for {
v, w := edgeNodesFor(rnd(nChoose2))
e := simple.Edge{F: v, T: w, W: 1}
if !hasEdge(e.F, e.T) {
dst.SetEdge(e)
break
}
}
}
return nil
}
func benchmarkAStarHeuristic(b *testing.B, g graph.Undirected, h Heuristic) {
var expanded int
for i := 0; i < b.N; i++ {
_, expanded = AStar(simple.Node(0), simple.Node(1), g, h)
}
if expanded == 0 {
b.Fatal("unexpected number of expanded nodes")
}
}
func undirectedEdgeAttrGraphFrom(g []set, attr map[edge][]Attribute) graph.Graph {
dg := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range g {
for v := range e {
dg.SetEdge(attrEdge{from: simple.Node(u), to: simple.Node(v), attr: attr[edge{from: u, to: v}]})
}
}
return dg
}
func undirectedGraphFrom(g []set) graph.Graph {
dg := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range g {
for v := range e {
dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
return dg
}
func TestReduceQConsistency(t *testing.T) {
tests:
for _, test := range communityQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
if math.IsNaN(structure.want) {
continue tests
}
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
sort.Sort(ordered.ByID(communities[i]))
}
gQ := Q(g, communities, structure.resolution)
gQnull := Q(g, nil, 1)
cg0 := reduce(g, nil)
cg0Qnull := Q(cg0, cg0.Structure(), 1)
if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
t.Errorf("disgagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
}
cg0Q := Q(cg0, communities, structure.resolution)
if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
t.Errorf("unexpected Q result after initial conversion: got: %v want :%v", gQ, cg0Q)
}
cg1 := reduce(cg0, communities)
cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
t.Errorf("unexpected Q result after initial condensation: got: %v want :%v", gQ, cg1Q)
}
}
}
}
// Nodes returns all the nodes in the grid.
func (l *LimitedVisionGrid) Nodes() []graph.Node {
nodes := make([]graph.Node, 0, len(l.Grid.open))
for id := range l.Grid.open {
nodes = append(nodes, simple.Node(id))
}
return nodes
}
// Nodes returns all the open nodes in the grid if AllVisible is
// false, otherwise all nodes are returned.
func (g *Grid) Nodes() []graph.Node {
var nodes []graph.Node
for id, ok := range g.open {
if ok || g.AllVisible {
nodes = append(nodes, simple.Node(id))
}
}
return nodes
}
func undirectedStructuredGraphFrom(c []edge, g ...[]set) graph.Graph {
s := &structuredGraph{UndirectedGraph: simple.NewUndirectedGraph(0, math.Inf(1))}
var base int
for i, sg := range g {
sub := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range sg {
for v := range e {
ce := simple.Edge{F: simple.Node(u + base), T: simple.Node(v + base)}
sub.SetEdge(ce)
}
}
s.sub = append(s.sub, namedGraph{id: i, Graph: sub})
base += len(sg)
}
for _, e := range c {
s.SetEdge(simple.Edge{F: simple.Node(e.from), T: simple.Node(e.to)})
}
return s
}
func TestNonContiguous(t *testing.T) {
g := simple.NewUndirectedGraph(0, 0)
for _, e := range []simple.Edge{
{F: simple.Node(0), T: simple.Node(1), W: 1},
{F: simple.Node(4), T: simple.Node(5), W: 1},
} {
g.SetEdge(e)
}
func() {
defer func() {
r := recover()
if r != nil {
t.Error("unexpected panic with non-contiguous ID range")
}
}()
Louvain(g, 1, nil)
}()
}
func TestWalkAll(t *testing.T) {
for i, test := range walkAllTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
if !g.Has(simple.Node(v)) {
g.AddNode(simple.Node(v))
}
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
type walker interface {
WalkAll(g graph.Undirected, before, after func(), during func(graph.Node))
}
for _, w := range []walker{
&BreadthFirst{},
&DepthFirst{},
} {
var (
c []graph.Node
cc [][]graph.Node
)
switch w := w.(type) {
case *BreadthFirst:
w.EdgeFilter = test.edge
case *DepthFirst:
w.EdgeFilter = test.edge
default:
panic(fmt.Sprintf("bad walker type: %T", w))
}
during := func(n graph.Node) {
c = append(c, n)
}
after := func() {
cc = append(cc, []graph.Node(nil))
cc[len(cc)-1] = append(cc[len(cc)-1], c...)
c = c[:0]
}
w.WalkAll(g, nil, after, during)
got := make([][]int, len(cc))
for j, c := range cc {
ids := make([]int, len(c))
for k, n := range c {
ids[k] = n.ID()
}
sort.Ints(ids)
got[j] = ids
}
sort.Sort(ordered.BySliceValues(got))
if !reflect.DeepEqual(got, test.want) {
t.Errorf("unexpected connected components for test %d using %T:\ngot: %v\nwant:%v", i, w, got, test.want)
}
}
}
}
func TestConnectedComponents(t *testing.T) {
for i, test := range connectedComponentTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
if !g.Has(simple.Node(v)) {
g.AddNode(simple.Node(v))
}
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
cc := ConnectedComponents(g)
got := make([][]int, len(cc))
for j, c := range cc {
ids := make([]int, len(c))
for k, n := range c {
ids[k] = n.ID()
}
sort.Ints(ids)
got[j] = ids
}
sort.Sort(ordered.BySliceValues(got))
if !reflect.DeepEqual(got, test.want) {
t.Errorf("unexpected connected components for test %d %T:\ngot: %v\nwant:%v", i, g, got, test.want)
}
}
}
func TestMoveLocal(t *testing.T) {
for _, test := range localMoveTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
sort.Sort(ordered.ByID(communities[i]))
}
r := reduce(reduce(g, nil), communities)
l := newLocalMover(r, r.communities, structure.resolution)
for _, n := range structure.targetNodes {
dQ, dst, src := l.deltaQ(n)
if dQ > 0 {
before := Q(r, l.communities, structure.resolution)
l.move(dst, src)
after := Q(r, l.communities, structure.resolution)
want := after - before
if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
}
}
}
}
}
}
// PreferentialAttachment constructs a graph in the destination, dst, of order n.
// The graph is constructed successively starting from an m order graph with one
// node having degree m-1. At each iteration of graph addition, one node is added
// with m additional edges joining existing nodes with probability proportional
// to the nodes' degrees. If src is not nil it is used as the random source,
// otherwise rand.Float64 is used.
//
// The algorithm is essentially as described in http://arxiv.org/abs/cond-mat/0110452
// after 10.1126/science.286.5439.509.
func PreferentialAttachment(dst graph.UndirectedBuilder, n, m int, src *rand.Rand) error {
if n <= m {
return fmt.Errorf("gen: n <= m: n=%v m=%d", n, m)
}
// Initial condition.
wt := make([]float64, n)
for u := 0; u < m; u++ {
if !dst.Has(simple.Node(u)) {
dst.AddNode(simple.Node(u))
}
// We need to give equal probability for
// adding the first generation of edges.
wt[u] = 1
}
ws := sample.NewWeighted(wt, src)
for i := range wt {
// These weights will organically grow
// after the first growth iteration.
wt[i] = 0
}
// Growth.
for v := m; v < n; v++ {
for i := 0; i < m; i++ {
// Preferential attachment.
u, ok := ws.Take()
if !ok {
return errors.New("gen: depleted distribution")
}
dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
wt[u]++
wt[v]++
}
ws.ReweightAll(wt)
}
return nil
}
func TestVertexOrdering(t *testing.T) {
for i, test := range vOrderTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
order, core := VertexOrdering(g)
if len(core)-1 != test.wantK {
t.Errorf("unexpected value of k for test %d: got: %d want: %d", i, len(core)-1, test.wantK)
}
var offset int
for k, want := range test.wantCore {
sort.Ints(want)
got := make([]int, len(want))
for j, n := range order[len(order)-len(want)-offset : len(order)-offset] {
got[j] = n.ID()
}
sort.Ints(got)
if !reflect.DeepEqual(got, want) {
t.Errorf("unexpected %d-core for test %d:\ngot: %v\nwant:%v", got, test.wantCore)
}
for j, n := range core[k] {
got[j] = n.ID()
}
sort.Ints(got)
if !reflect.DeepEqual(got, want) {
t.Errorf("unexpected %d-core for test %d:\ngot: %v\nwant:%v", got, test.wantCore)
}
offset += len(want)
}
}
}
func TestIsPath(t *testing.T) {
dg := simple.NewDirectedGraph(0, math.Inf(1))
if !IsPathIn(dg, nil) {
t.Error("IsPath returns false on nil path")
}
p := []graph.Node{simple.Node(0)}
if IsPathIn(dg, p) {
t.Error("IsPath returns true on nonexistant node")
}
dg.AddNode(p[0])
if !IsPathIn(dg, p) {
t.Error("IsPath returns false on single-length path with existing node")
}
p = append(p, simple.Node(1))
dg.AddNode(p[1])
if IsPathIn(dg, p) {
t.Error("IsPath returns true on bad path of length 2")
}
dg.SetEdge(simple.Edge{F: p[0], T: p[1], W: 1})
if !IsPathIn(dg, p) {
t.Error("IsPath returns false on correct path of length 2")
}
p[0], p[1] = p[1], p[0]
if IsPathIn(dg, p) {
t.Error("IsPath erroneously returns true for a reverse path")
}
p = []graph.Node{p[1], p[0], simple.Node(2)}
dg.SetEdge(simple.Edge{F: p[1], T: p[2], W: 1})
if !IsPathIn(dg, p) {
t.Error("IsPath does not find a correct path for path > 2 nodes")
}
ug := simple.NewUndirectedGraph(0, math.Inf(1))
ug.SetEdge(simple.Edge{F: p[1], T: p[0], W: 1})
ug.SetEdge(simple.Edge{F: p[1], T: p[2], W: 1})
if !IsPathIn(dg, p) {
t.Error("IsPath does not correctly account for undirected behavior")
}
}
func TestPageRankSparse(t *testing.T) {
for i, test := range pageRankTests {
g := simple.NewDirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
got := PageRankSparse(g, test.damp, test.tol)
prec := 1 - int(math.Log10(test.wantTol))
for n := range test.g {
if !floats.EqualWithinAbsOrRel(got[n], test.want[n], test.wantTol, test.wantTol) {
t.Errorf("unexpected PageRank result for test %d:\ngot: %v\nwant:%v",
i, orderedFloats(got, prec), orderedFloats(test.want, prec))
break
}
}
}
}
func TestBreadthFirst(t *testing.T) {
for i, test := range breadthFirstTests {
g := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
}
}
w := BreadthFirst{
EdgeFilter: test.edge,
}
var got [][]int
final := w.Walk(g, test.from, func(n graph.Node, d int) bool {
if test.until != nil && test.until(n, d) {
return true
}
if d >= len(got) {
got = append(got, []int(nil))
}
got[d] = append(got[d], n.ID())
return false
})
if !test.final[final] {
t.Errorf("unexepected final node for test %d:\ngot: %v\nwant: %v", i, final, test.final)
}
for _, l := range got {
sort.Ints(l)
}
if !reflect.DeepEqual(got, test.want) {
t.Errorf("unexepected BFS level structure for test %d:\ngot: %v\nwant: %v", i, got, test.want)
}
}
}
func undirectedSubGraphFrom(g []set, s map[int][]set) graph.Graph {
var base int
subs := make(map[int]subGraph)
for i, sg := range s {
sub := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range sg {
for v := range e {
ce := simple.Edge{F: simple.Node(u + base), T: simple.Node(v + base)}
sub.SetEdge(ce)
}
}
subs[i] = subGraph{id: i, Graph: sub}
base += len(sg)
}
dg := simple.NewUndirectedGraph(0, math.Inf(1))
for u, e := range g {
var nu graph.Node
if sg, ok := subs[u]; ok {
sg.id += base
nu = sg
} else {
nu = simple.Node(u + base)
}
for v := range e {
var nv graph.Node
if sg, ok := subs[v]; ok {
sg.id += base
nv = sg
} else {
nv = simple.Node(v + base)
}
dg.SetEdge(simple.Edge{F: nu, T: nv})
}
}
return dg
}
