// HITS returns the Hyperlink-Induced Topic Search hub-authority scores for
// nodes of the directed graph g. HITS terminates when the 2-norm of the
// vector difference between iterations is below tol. The returned map is
// keyed on the graph node IDs.
func HITS(g graph.Directed, tol float64) map[int]HubAuthority {
nodes := g.Nodes()
// Make a topological copy of g with dense node IDs.
indexOf := make(map[int]int, len(nodes))
for i, n := range nodes {
indexOf[n.ID()] = i
}
nodesLinkingTo := make([][]int, len(nodes))
nodesLinkedFrom := make([][]int, len(nodes))
for i, n := range nodes {
for _, u := range g.To(n) {
nodesLinkingTo[i] = append(nodesLinkingTo[i], indexOf[u.ID()])
}
for _, v := range g.From(n) {
nodesLinkedFrom[i] = append(nodesLinkedFrom[i], indexOf[v.ID()])
}
}
indexOf = nil
w := make([]float64, 4*len(nodes))
auth := w[:len(nodes)]
hub := w[len(nodes) : 2*len(nodes)]
for i := range nodes {
auth[i] = 1
hub[i] = 1
}
deltaAuth := w[2*len(nodes) : 3*len(nodes)]
deltaHub := w[3*len(nodes):]
var norm float64
for {
norm = 0
for v := range nodes {
var a float64
for _, u := range nodesLinkingTo[v] {
a += hub[u]
}
deltaAuth[v] = auth[v]
auth[v] = a
norm += a * a
}
norm = math.Sqrt(norm)
for i := range auth {
auth[i] /= norm
deltaAuth[i] -= auth[i]
}
norm = 0
for u := range nodes {
var h float64
for _, v := range nodesLinkedFrom[u] {
h += auth[v]
}
deltaHub[u] = hub[u]
hub[u] = h
norm += h * h
}
norm = math.Sqrt(norm)
for i := range hub {
hub[i] /= norm
deltaHub[i] -= hub[i]
}
if floats.Norm(deltaAuth, 2) < tol && floats.Norm(deltaHub, 2) < tol {
break
}
}
hubAuth := make(map[int]HubAuthority, len(nodes))
for i, n := range nodes {
hubAuth[n.ID()] = HubAuthority{Hub: hub[i], Authority: auth[i]}
}
return hubAuth
}
