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266 lines
6.4 KiB
Go
266 lines
6.4 KiB
Go
package autopilot
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import (
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"fmt"
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"sync"
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)
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// stack is a simple int stack to help with readability of Brandes'
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// betweenness centrality implementation below.
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type stack struct {
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stack []int
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}
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func (s *stack) push(v int) {
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s.stack = append(s.stack, v)
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}
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func (s *stack) top() int {
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return s.stack[len(s.stack)-1]
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}
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func (s *stack) pop() {
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s.stack = s.stack[:len(s.stack)-1]
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}
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func (s *stack) empty() bool {
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return len(s.stack) == 0
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}
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// queue is a simple int queue to help with readability of Brandes'
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// betweenness centrality implementation below.
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type queue struct {
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queue []int
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}
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func (q *queue) push(v int) {
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q.queue = append(q.queue, v)
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}
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func (q *queue) front() int {
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return q.queue[0]
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}
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func (q *queue) pop() {
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q.queue = q.queue[1:]
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}
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func (q *queue) empty() bool {
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return len(q.queue) == 0
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}
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// BetweennessCentrality is a NodeMetric that calculates node betweenness
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// centrality using Brandes' algorithm. Betweenness centrality for each node
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// is the number of shortest paths passing trough that node, not counting
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// shortest paths starting or ending at that node. This is a useful metric
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// to measure control of individual nodes over the whole network.
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type BetweennessCentrality struct {
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// workers number of goroutines are used to parallelize
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// centrality calculation.
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workers int
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// centrality stores original (not normalized) centrality values for
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// each node in the graph.
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centrality map[NodeID]float64
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// min is the minimum centrality in the graph.
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min float64
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// max is the maximum centrality in the graph.
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max float64
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}
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// NewBetweennessCentralityMetric creates a new BetweennessCentrality instance.
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// Users can specify the number of workers to use for calculating centrality.
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func NewBetweennessCentralityMetric(workers int) (*BetweennessCentrality, error) {
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// There should be at least one worker.
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if workers < 1 {
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return nil, fmt.Errorf("workers must be positive")
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}
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return &BetweennessCentrality{
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workers: workers,
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}, nil
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}
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// Name returns the name of the metric.
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func (bc *BetweennessCentrality) Name() string {
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return "betweenness_centrality"
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}
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// betweennessCentrality is the core of Brandes' algorithm.
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// We first calculate the shortest paths from the start node s to all other
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// nodes with BFS, then update the betweenness centrality values by using
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// Brandes' dependency trick.
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// For detailed explanation please read:
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// https://www.cl.cam.ac.uk/teaching/1617/MLRD/handbook/brandes.html
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func betweennessCentrality(g *SimpleGraph, s int, centrality []float64) {
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// pred[w] is the list of nodes that immediately precede w on a
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// shortest path from s to t for each node t.
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pred := make([][]int, len(g.Nodes))
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// sigma[t] is the number of shortest paths between nodes s and t
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// for each node t.
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sigma := make([]int, len(g.Nodes))
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sigma[s] = 1
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// dist[t] holds the distance between s and t for each node t.
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// We initialize this to -1 (meaning infinity) for each t != s.
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dist := make([]int, len(g.Nodes))
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for i := range dist {
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dist[i] = -1
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}
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dist[s] = 0
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var (
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st stack
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q queue
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)
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q.push(s)
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// BFS to calculate the shortest paths (sigma and pred)
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// from s to t for each node t.
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for !q.empty() {
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v := q.front()
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q.pop()
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st.push(v)
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for _, w := range g.Adj[v] {
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// If distance from s to w is infinity (-1)
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// then set it and enqueue w.
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if dist[w] < 0 {
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dist[w] = dist[v] + 1
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q.push(w)
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}
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// If w is on a shortest path the update
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// sigma and add v to w's predecessor list.
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if dist[w] == dist[v]+1 {
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sigma[w] += sigma[v]
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pred[w] = append(pred[w], v)
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}
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}
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}
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// delta[v] is the ratio of the shortest paths between s and t that go
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// through v and the total number of shortest paths between s and t.
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// If we have delta then the betweenness centrality is simply the sum
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// of delta[w] for each w != s.
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delta := make([]float64, len(g.Nodes))
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for !st.empty() {
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w := st.top()
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st.pop()
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// pred[w] is the list of nodes that immediately precede w on a
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// shortest path from s.
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for _, v := range pred[w] {
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// Update delta using Brandes' equation.
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delta[v] += (float64(sigma[v]) / float64(sigma[w])) * (1.0 + delta[w])
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}
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if w != s {
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// As noted above centrality is simply the sum
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// of delta[w] for each w != s.
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centrality[w] += delta[w]
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}
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}
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}
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// Refresh recaculates and stores centrality values.
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func (bc *BetweennessCentrality) Refresh(graph ChannelGraph) error {
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cache, err := NewSimpleGraph(graph)
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if err != nil {
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return err
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}
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var wg sync.WaitGroup
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work := make(chan int)
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partials := make(chan []float64, bc.workers)
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// Each worker will compute a partial result.
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// This partial result is a sum of centrality updates
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// on roughly N / workers nodes.
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worker := func() {
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defer wg.Done()
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partial := make([]float64, len(cache.Nodes))
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// Consume the next node, update centrality
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// parital to avoid unnecessary synchronizaton.
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for node := range work {
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betweennessCentrality(cache, node, partial)
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}
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partials <- partial
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}
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// Now start the N workers.
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wg.Add(bc.workers)
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for i := 0; i < bc.workers; i++ {
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go worker()
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}
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// Distribute work amongst workers.
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// Should be fair when the graph is sufficiently large.
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for node := range cache.Nodes {
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work <- node
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}
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close(work)
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wg.Wait()
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close(partials)
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// Collect and sum partials for final result.
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centrality := make([]float64, len(cache.Nodes))
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for partial := range partials {
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for i := 0; i < len(partial); i++ {
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centrality[i] += partial[i]
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}
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}
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// Get min/max to be able to normalize
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// centrality values between 0 and 1.
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bc.min = 0
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bc.max = 0
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if len(centrality) > 0 {
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for _, v := range centrality {
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if v < bc.min {
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bc.min = v
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} else if v > bc.max {
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bc.max = v
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}
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}
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}
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// Divide by two as this is an undirected graph.
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bc.min /= 2.0
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bc.max /= 2.0
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bc.centrality = make(map[NodeID]float64)
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for u, value := range centrality {
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// Divide by two as this is an undirected graph.
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bc.centrality[cache.Nodes[u]] = value / 2.0
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}
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return nil
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}
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// GetMetric returns the current centrality values for each node indexed
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// by node id.
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func (bc *BetweennessCentrality) GetMetric(normalize bool) map[NodeID]float64 {
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// Normalization factor.
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var z float64
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if (bc.max - bc.min) > 0 {
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z = 1.0 / (bc.max - bc.min)
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}
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centrality := make(map[NodeID]float64)
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for k, v := range bc.centrality {
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if normalize {
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v = (v - bc.min) * z
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}
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centrality[k] = v
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}
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return centrality
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}
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