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| 1 | +// File: src/centrality/algorithms.rs |
| 2 | + |
| 3 | +use crate::graph::types::{BaseGraph, NodeId}; |
| 4 | +use crate::paths::algorithms::dijkstra; // Our dijkstra implementation |
| 5 | +use ordered_float::OrderedFloat; |
| 6 | +use std::collections::VecDeque; |
| 7 | + |
| 8 | +/// ### Degree Centrality |
| 9 | +/// For each node, degree centrality is defined as the sum of its out-degree and in-degree. |
| 10 | +pub fn degree_centrality<A, W, Ty>(graph: &BaseGraph<A, W, Ty>) -> Vec<f64> |
| 11 | +where |
| 12 | + W: Copy, |
| 13 | + Ty: crate::graph::types::GraphConstructor<A, W>, |
| 14 | +{ |
| 15 | + let n = graph.node_count(); |
| 16 | + let mut degree = vec![0usize; n]; |
| 17 | + // Out-degree: count neighbors for each node. |
| 18 | + for (node, _) in graph.nodes() { |
| 19 | + let outdeg = graph.neighbors(node).count(); |
| 20 | + degree[node.index()] += outdeg; |
| 21 | + } |
| 22 | + // In-degree: count each appearance as target in edges. |
| 23 | + for (_u, v, _w) in graph.edges() { |
| 24 | + degree[v.index()] += 1; |
| 25 | + } |
| 26 | + degree.into_iter().map(|d| d as f64).collect() |
| 27 | +} |
| 28 | + |
| 29 | +/// ### Closeness Centrality |
| 30 | +/// For each node, closeness centrality is defined as (n-1) divided by the sum of shortest-path |
| 31 | +/// distances from that node to all other nodes. (If a node cannot reach all others, its centrality is 0.) |
| 32 | +/// This implementation uses our dijkstra algorithm, so it requires the graph’s weight type to be |
| 33 | +/// `OrderedFloat<f64>`. |
| 34 | +pub fn closeness_centrality<A, Ty>(graph: &BaseGraph<A, OrderedFloat<f64>, Ty>) -> Vec<f64> |
| 35 | +where |
| 36 | + Ty: crate::graph::types::GraphConstructor<A, OrderedFloat<f64>>, |
| 37 | +{ |
| 38 | + let n = graph.node_count(); |
| 39 | + let mut closeness = vec![0.0; n]; |
| 40 | + for (node, _) in graph.nodes() { |
| 41 | + let distances = dijkstra(graph, node); |
| 42 | + let sum: f64 = distances.iter().filter_map(|&d| d.map(|od| od.0)).sum(); |
| 43 | + if sum > 0.0 { |
| 44 | + closeness[node.index()] = (n as f64 - 1.0) / sum; |
| 45 | + } else { |
| 46 | + closeness[node.index()] = 0.0; |
| 47 | + } |
| 48 | + } |
| 49 | + closeness |
| 50 | +} |
| 51 | + |
| 52 | +/// ### Betweenness Centrality (Unweighted) |
| 53 | +/// Using Brandes’ algorithm (based on BFS). |
| 54 | +/// Note: This is an unweighted implementation. |
| 55 | +pub fn betweenness_centrality<A, Ty>(graph: &BaseGraph<A, f64, Ty>) -> Vec<f64> |
| 56 | +where |
| 57 | + Ty: crate::graph::types::GraphConstructor<A, f64>, |
| 58 | +{ |
| 59 | + let n = graph.node_count(); |
| 60 | + let mut bc = vec![0.0; n]; |
| 61 | + |
| 62 | + // For each source node s: |
| 63 | + for (s, _) in graph.nodes() { |
| 64 | + let mut stack = Vec::new(); |
| 65 | + let mut pred: Vec<Vec<NodeId>> = vec![Vec::new(); n]; |
| 66 | + let mut sigma = vec![0.0; n]; // Number of shortest paths from s. |
| 67 | + let mut dist = vec![-1.0; n]; // Distance from s (-1 means infinity). |
| 68 | + sigma[s.index()] = 1.0; |
| 69 | + dist[s.index()] = 0.0; |
| 70 | + let mut queue = VecDeque::new(); |
| 71 | + queue.push_back(s); |
| 72 | + |
| 73 | + while let Some(v) = queue.pop_front() { |
| 74 | + stack.push(v); |
| 75 | + for w in graph.neighbors(v) { |
| 76 | + if dist[w.index()] < 0.0 { |
| 77 | + dist[w.index()] = dist[v.index()] + 1.0; |
| 78 | + queue.push_back(w); |
| 79 | + } |
| 80 | + if dist[w.index()] == dist[v.index()] + 1.0 { |
| 81 | + sigma[w.index()] += sigma[v.index()]; |
| 82 | + pred[w.index()].push(v); |
| 83 | + } |
| 84 | + } |
| 85 | + } |
| 86 | + |
| 87 | + let mut delta = vec![0.0; n]; |
| 88 | + while let Some(w) = stack.pop() { |
| 89 | + for &v in &pred[w.index()] { |
| 90 | + delta[v.index()] += |
| 91 | + (sigma[v.index()] / sigma[w.index()]) * (1.0 + delta[w.index()]); |
| 92 | + } |
| 93 | + if w != s { |
| 94 | + bc[w.index()] += delta[w.index()]; |
| 95 | + } |
| 96 | + } |
| 97 | + } |
| 98 | + bc |
| 99 | +} |
| 100 | + |
| 101 | +/// ### Eigenvector Centrality |
| 102 | +/// Computes centrality via power iteration over the adjacency matrix. |
| 103 | +/// This implementation uses plain f64. |
| 104 | +pub fn eigenvector_centrality<A, Ty>(graph: &BaseGraph<A, f64, Ty>, iterations: usize) -> Vec<f64> |
| 105 | +where |
| 106 | + Ty: crate::graph::types::GraphConstructor<A, f64>, |
| 107 | +{ |
| 108 | + let n = graph.node_count(); |
| 109 | + let mut centrality = vec![1.0; n]; |
| 110 | + for _ in 0..iterations { |
| 111 | + let mut next = vec![0.0; n]; |
| 112 | + for (node, _) in graph.nodes() { |
| 113 | + for neighbor in graph.neighbors(node) { |
| 114 | + next[neighbor.index()] += centrality[node.index()]; |
| 115 | + } |
| 116 | + } |
| 117 | + let norm = next.iter().map(|x| x * x).sum::<f64>().sqrt(); |
| 118 | + if norm > 0.0 { |
| 119 | + for x in next.iter_mut() { |
| 120 | + *x /= norm; |
| 121 | + } |
| 122 | + } |
| 123 | + centrality = next; |
| 124 | + } |
| 125 | + centrality |
| 126 | +} |
| 127 | + |
| 128 | +/// ### PageRank |
| 129 | +/// Computes PageRank scores using iterative updates with damping. |
| 130 | +pub fn pagerank<A, Ty>(graph: &BaseGraph<A, f64, Ty>, damping: f64, iterations: usize) -> Vec<f64> |
| 131 | +where |
| 132 | + Ty: crate::graph::types::GraphConstructor<A, f64>, |
| 133 | +{ |
| 134 | + let n = graph.node_count(); |
| 135 | + let mut rank = vec![1.0 / n as f64; n]; |
| 136 | + let teleport = (1.0 - damping) / n as f64; |
| 137 | + |
| 138 | + // Precompute out-degree for each node. |
| 139 | + let mut out_deg = vec![0usize; n]; |
| 140 | + for (node, _) in graph.nodes() { |
| 141 | + out_deg[node.index()] = graph.neighbors(node).count(); |
| 142 | + } |
| 143 | + |
| 144 | + for _ in 0..iterations { |
| 145 | + let mut new_rank = vec![teleport; n]; |
| 146 | + for (u, _) in graph.nodes() { |
| 147 | + let r = rank[u.index()]; |
| 148 | + if out_deg[u.index()] > 0 { |
| 149 | + let share = damping * r / out_deg[u.index()] as f64; |
| 150 | + for v in graph.neighbors(u) { |
| 151 | + new_rank[v.index()] += share; |
| 152 | + } |
| 153 | + } else { |
| 154 | + // Distribute uniformly if no out-edges. |
| 155 | + for x in new_rank.iter_mut() { |
| 156 | + *x += damping * r / n as f64; |
| 157 | + } |
| 158 | + } |
| 159 | + } |
| 160 | + rank = new_rank; |
| 161 | + } |
| 162 | + rank |
| 163 | +} |
| 164 | + |
| 165 | +/// ### Katz Centrality |
| 166 | +/// Computes centrality using the formula: x = alpha * A * x + beta. |
| 167 | +/// beta is a constant offset for each node. |
| 168 | +pub fn katz_centrality<A, Ty>( |
| 169 | + graph: &BaseGraph<A, f64, Ty>, |
| 170 | + alpha: f64, |
| 171 | + beta: f64, |
| 172 | + iterations: usize, |
| 173 | +) -> Vec<f64> |
| 174 | +where |
| 175 | + Ty: crate::graph::types::GraphConstructor<A, f64>, |
| 176 | +{ |
| 177 | + let n = graph.node_count(); |
| 178 | + let mut centrality = vec![beta; n]; |
| 179 | + for _ in 0..iterations { |
| 180 | + let mut next = vec![beta; n]; |
| 181 | + for (node, _) in graph.nodes() { |
| 182 | + for neighbor in graph.neighbors(node) { |
| 183 | + next[neighbor.index()] += alpha * centrality[node.index()]; |
| 184 | + } |
| 185 | + } |
| 186 | + let norm: f64 = next.iter().map(|&x| x * x).sum::<f64>().sqrt(); |
| 187 | + if norm > 0.0 { |
| 188 | + for x in next.iter_mut() { |
| 189 | + *x /= norm; |
| 190 | + } |
| 191 | + } |
| 192 | + centrality = next; |
| 193 | + } |
| 194 | + centrality |
| 195 | +} |
| 196 | + |
| 197 | +/// ### Harmonic Centrality |
| 198 | +/// For each node, harmonic centrality is defined as the sum of the reciprocals of the shortest |
| 199 | +/// path distances to all other nodes (ignoring unreachable nodes). Uses dijkstra, |
| 200 | +/// so requires weights to be OrderedFloat<f64>. |
| 201 | +pub fn harmonic_centrality<A, Ty>(graph: &BaseGraph<A, OrderedFloat<f64>, Ty>) -> Vec<f64> |
| 202 | +where |
| 203 | + Ty: crate::graph::types::GraphConstructor<A, OrderedFloat<f64>>, |
| 204 | +{ |
| 205 | + let n = graph.node_count(); |
| 206 | + let mut centrality = vec![0.0; n]; |
| 207 | + for (node, _) in graph.nodes() { |
| 208 | + let distances = dijkstra(graph, node); |
| 209 | + let sum: f64 = distances |
| 210 | + .iter() |
| 211 | + .filter_map(|&d| d.map(|od| od.0)) |
| 212 | + .filter(|&d| d > 0.0) |
| 213 | + .map(|d| 1.0 / d) |
| 214 | + .sum(); |
| 215 | + centrality[node.index()] = sum; |
| 216 | + } |
| 217 | + centrality |
| 218 | +} |
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