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// Copyright ©2017 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 spectral
import (
"math"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/mat"
)
// Laplacian is a graph Laplacian matrix.
type Laplacian struct {
// Matrix holds the Laplacian matrix.
mat.Matrix
// Nodes holds the input graph nodes.
Nodes []graph.Node
// Index is a mapping from the graph
// node IDs to row and column indices.
Index map[int64]int
}
// NewLaplacian returns a Laplacian matrix for the simple undirected graph g.
// The Laplacian is defined as D-A where D is a diagonal matrix holding the
// degree of each node and A is the graph adjacency matrix of the input graph.
// If g contains self edges, NewLaplacian will panic.
func NewLaplacian(g graph.Undirected) Laplacian {
nodes := graph.NodesOf(g.Nodes())
indexOf := make(map[int64]int, len(nodes))
for i, n := range nodes {
id := n.ID()
indexOf[id] = i
}
l := mat.NewSymDense(len(nodes), nil)
for j, u := range nodes {
uid := u.ID()
to := graph.NodesOf(g.From(uid))
l.SetSym(j, j, float64(len(to)))
for _, v := range to {
vid := v.ID()
if uid == vid {
panic("network: self edge in graph")
}
if uid < vid {
l.SetSym(indexOf[vid], j, -1)
}
}
}
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
}
// NewSymNormLaplacian returns a symmetric normalized Laplacian matrix for the
// simple undirected graph g.
// The normalized Laplacian is defined as I-D^(-1/2)AD^(-1/2) where D is a
// diagonal matrix holding the degree of each node and A is the graph adjacency
// matrix of the input graph.
// If g contains self edges, NewSymNormLaplacian will panic.
func NewSymNormLaplacian(g graph.Undirected) Laplacian {
nodes := graph.NodesOf(g.Nodes())
indexOf := make(map[int64]int, len(nodes))
for i, n := range nodes {
id := n.ID()
indexOf[id] = i
}
l := mat.NewSymDense(len(nodes), nil)
for j, u := range nodes {
uid := u.ID()
to := graph.NodesOf(g.From(uid))
if len(to) == 0 {
continue
}
l.SetSym(j, j, 1)
squdeg := math.Sqrt(float64(len(to)))
for _, v := range to {
vid := v.ID()
if uid == vid {
panic("network: self edge in graph")
}
if uid < vid {
to := g.From(vid)
k := to.Len()
if k < 0 {
k = len(graph.NodesOf(to))
}
l.SetSym(indexOf[vid], j, -1/(squdeg*math.Sqrt(float64(k))))
}
}
}
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
}
// NewRandomWalkLaplacian returns a damp-scaled random walk Laplacian matrix for
// the simple graph g.
// The random walk Laplacian is defined as I-D^(-1)A where D is a diagonal matrix
// holding the degree of each node and A is the graph adjacency matrix of the input
// graph.
// If g contains self edges, NewRandomWalkLaplacian will panic.
func NewRandomWalkLaplacian(g graph.Graph, damp float64) Laplacian {
nodes := graph.NodesOf(g.Nodes())
indexOf := make(map[int64]int, len(nodes))
for i, n := range nodes {
id := n.ID()
indexOf[id] = i
}
l := mat.NewDense(len(nodes), len(nodes), nil)
for j, u := range nodes {
uid := u.ID()
to := graph.NodesOf(g.From(uid))
if len(to) == 0 {
continue
}
l.Set(j, j, 1-damp)
rudeg := (damp - 1) / float64(len(to))
for _, v := range to {
vid := v.ID()
if uid == vid {
panic("network: self edge in graph")
}
l.Set(indexOf[vid], j, rudeg)
}
}
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
}
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