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| 1 | /* | |
| 2 | * Copyright (c) 2003, the JUNG Project and the Regents of the University | |
| 3 | * of California | |
| 4 | * All rights reserved. | |
| 5 | * | |
| 6 | * This software is open-source under the BSD license; see either | |
| 7 | * "license.txt" or | |
| 8 | * http://jung.sourceforge.net/license.txt for a description. | |
| 9 | */ | |
| 10 | package edu.uci.ics.jung.random.generators; | |
| 11 | ||
| 12 | import java.util.HashMap; | |
| 13 | import java.util.HashSet; | |
| 14 | import java.util.Iterator; | |
| 15 | import java.util.LinkedList; | |
| 16 | import java.util.List; | |
| 17 | import java.util.Map; | |
| 18 | import java.util.Random; | |
| 19 | import java.util.Set; | |
| 20 | import java.util.Vector; | |
| 21 | ||
| 22 | import edu.uci.ics.jung.graph.ArchetypeGraph; | |
| 23 | import edu.uci.ics.jung.graph.Edge; | |
| 24 | import edu.uci.ics.jung.graph.Graph; | |
| 25 | import edu.uci.ics.jung.graph.Vertex; | |
| 26 | import edu.uci.ics.jung.graph.impl.DirectedSparseEdge; | |
| 27 | import edu.uci.ics.jung.graph.impl.DirectedSparseGraph; | |
| 28 | import edu.uci.ics.jung.graph.impl.DirectedSparseVertex; | |
| 29 | import edu.uci.ics.jung.graph.impl.UndirectedSparseEdge; | |
| 30 | import edu.uci.ics.jung.graph.impl.UndirectedSparseGraph; | |
| 31 | import edu.uci.ics.jung.graph.impl.UndirectedSparseVertex; | |
| 32 | import edu.uci.ics.jung.utils.Pair; | |
| 33 | import edu.uci.ics.jung.utils.UserData; | |
| 34 | ||
| 35 | /** | |
| 36 | * <p>Simple evolving scale-free random graph generator. At each time | |
| 37 | * step, a new vertex is created and is connected to existing vertices | |
| 38 | * according to the principle of "preferential attachment", whereby | |
| 39 | * vertices with higher degree have a higher probability of being | |
| 40 | * selected for attachment.</p> | |
| 41 | * | |
| 42 | * <p>At a given timestep, the probability <code>p</code> of creating an edge | |
| 43 | * between an existing vertex <code>v</code> and the newly added vertex is | |
| 44 | * <pre> | |
| 45 | * p = (degree(v) + 1) / (|E| + |V|); | |
| 46 | * </pre> | |
| 47 | * | |
| 48 | * <p>where <code>|E|</code> and <code>|V|</code> are, respectively, the number | |
| 49 | * of edges and vertices currently in the network (counting neither the new | |
| 50 | * vertex nor the other edges that are being attached to it).</p> | |
| 51 | * | |
| 52 | * <p>Note that the formula specified in the original paper | |
| 53 | * (cited below) was | |
| 54 | * <pre> | |
| 55 | * p = degree(v) / |E| | |
| 56 | * </pre> | |
| 57 | * </p> | |
| 58 | * | |
| 59 | * <p>However, this would have meant that the probability of attachment for any existing | |
| 60 | * isolated vertex would be 0. This version uses Lagrangian smoothing to give | |
| 61 | * each existing vertex a positive attachment probability.</p> | |
| 62 | * | |
| 63 | * <p>The graph created may be either directed or undirected (controlled by a constructor | |
| 64 | * parameter); the default is undirected. | |
| 65 | * If the graph is specified to be directed, then the edges added will be directed | |
| 66 | * from the newly added vertex u to the existing vertex v, with probability proportional to the | |
| 67 | * indegree of v (number of edges directed towards v). If the graph is specified to be undirected, | |
| 68 | * then the (undirected) edges added will connect u to v, with probability proportional to the | |
| 69 | * degree of v.</p> | |
| 70 | * | |
| 71 | * <p>The <code>parallel</code> constructor parameter specifies whether parallel edges | |
| 72 | * may be created.</p> | |
| 73 | * | |
| 74 | * @see "A.-L. Barabasi and R. Albert, Emergence of scaling in random networks, Science 286, 1999." | |
| 75 | * @author Scott White | |
| 76 | * @author Joshua O'Madadhain | |
| 77 | */ | |
| 78 | public class BarabasiAlbertGenerator implements EvolvingGraphGenerator | |
| 79 | { | |
| 80 | 1 | private Graph mGraph = null; |
| 81 | private int mNumEdgesToAttachPerStep; | |
| 82 | private int mElapsedTimeSteps; | |
| 83 | private Random mRandom; | |
| 84 | protected Vector vertex_index; | |
| 85 | protected int init_vertices; | |
| 86 | protected Map index_vertex; | |
| 87 | protected boolean directed; | |
| 88 | protected boolean parallel; | |
| 89 | ||
| 90 | /** | |
| 91 | * Tags the initial "seed" vertices that the graph starts with | |
| 92 | */ | |
| 93 | 1 | public final static Object SEED = "edu.uci.ics.jung.random.generators.BarabasiAlbertGenerator.SEED"; |
| 94 | ||
| 95 | /** | |
| 96 | * Constructs a new instance of the generator. | |
| 97 | * @param init_vertices number of unconnected 'seed' vertices that the graph should start with | |
| 98 | * @param numEdgesToAttach the number of edges that should be attached from the | |
| 99 | * new vertex to pre-existing vertices at each time step | |
| 100 | * @param directed specifies whether the graph and edges to be created should be directed or not | |
| 101 | * @param parallel specifies whether the algorithm permits parallel edges | |
| 102 | * @param seed random number seed | |
| 103 | */ | |
| 104 | public BarabasiAlbertGenerator(int init_vertices, int numEdgesToAttach, boolean directed, boolean parallel, int seed) | |
| 105 | 1 | { |
| 106 | 1 | if (init_vertices <= 0) |
| 107 | 0 | throw new IllegalArgumentException("Number of initial unconnected 'seed' vertices " + |
| 108 | "must be positive"); | |
| 109 | 1 | if (numEdgesToAttach <= 0) |
| 110 | 0 | throw new IllegalArgumentException("Number of edges to attach " + |
| 111 | "at each time step must be positive"); | |
| 112 | ||
| 113 | 1 | if (!parallel && init_vertices < numEdgesToAttach) |
| 114 | 0 | throw new IllegalArgumentException("If parallel edges disallowed, initial" + |
| 115 | "number of vertices must be >= number of edges to attach at each time step"); | |
| 116 | 1 | mNumEdgesToAttachPerStep = numEdgesToAttach; |
| 117 | 1 | mRandom = new Random(seed); |
| 118 | 1 | this.init_vertices = init_vertices; |
| 119 | 1 | this.directed = directed; |
| 120 | 1 | this.parallel = parallel; |
| 121 | 1 | initialize(); |
| 122 | 1 | } |
| 123 | ||
| 124 | /** | |
| 125 | * Constructs a new instance of the generator, whose output will be an undirected graph. | |
| 126 | * @param init_vertices number of unconnected 'seed' vertices that the graph should start with | |
| 127 | * @param numEdgesToAttach the number of edges that should be attached from the | |
| 128 | * new vertex to pre-existing vertices at each time step | |
| 129 | * @param seed random number seed | |
| 130 | */ | |
| 131 | public BarabasiAlbertGenerator(int init_vertices, int numEdgesToAttach, int seed) | |
| 132 | { | |
| 133 | 1 | this(init_vertices, numEdgesToAttach, false, false, seed); |
| 134 | 1 | } |
| 135 | ||
| 136 | /** | |
| 137 | * Constructs a new instance of the generator, whose output will be an undirected graph, | |
| 138 | * and which will use the current time as a seed for the random number generation. | |
| 139 | * @param init_vertices number of vertices that the graph should start with | |
| 140 | * @param numEdgesToAttach the number of edges that should be attached from the | |
| 141 | * new vertex to pre-existing vertices at each time step | |
| 142 | */ | |
| 143 | public BarabasiAlbertGenerator(int init_vertices, int numEdgesToAttach) { | |
| 144 | 0 | this(init_vertices, numEdgesToAttach, (int) System.currentTimeMillis()); |
| 145 | 0 | } |
| 146 | ||
| 147 | private void initialize() | |
| 148 | { | |
| 149 | 1 | if (directed) |
| 150 | 0 | mGraph = new DirectedSparseGraph(); |
| 151 | else | |
| 152 | 1 | mGraph = new UndirectedSparseGraph(); |
| 153 | 1 | if (parallel) |
| 154 | 0 | mGraph.getEdgeConstraints().remove(Graph.NOT_PARALLEL_EDGE); |
| 155 | 1 | vertex_index = new Vector(2*init_vertices); |
| 156 | 1 | index_vertex = new HashMap(2*init_vertices); |
| 157 | 2 | for (int i = 0; i < init_vertices; i++) |
| 158 | { | |
| 159 | 1 | Vertex v = new UndirectedSparseVertex(); |
| 160 | 1 | mGraph.addVertex(v); |
| 161 | 1 | vertex_index.add(v); |
| 162 | 1 | index_vertex.put(v, new Integer(i)); |
| 163 | 1 | v.addUserDatum(SEED, SEED, UserData.REMOVE); |
| 164 | } | |
| 165 | ||
| 166 | 1 | mElapsedTimeSteps = 0; |
| 167 | 1 | } |
| 168 | ||
| 169 | private Edge createRandomEdge(Set preexistingNodes, Vertex newVertex, Set added_pairs) | |
| 170 | { | |
| 171 | Vertex attach_point; | |
| 172 | 100 | boolean created_edge = false; |
| 173 | Pair endpoints; | |
| 174 | do | |
| 175 | { | |
| 176 | 3166 | attach_point = (Vertex)vertex_index.elementAt(mRandom.nextInt(vertex_index.size())); |
| 177 | ||
| 178 | 3166 | endpoints = new Pair(newVertex, attach_point); |
| 179 | ||
| 180 | // if parallel edges are not allowed, skip attach_point if <newVertex, attach_point> | |
| 181 | // already exists; note that because of the way edges are added, we only need to check | |
| 182 | // the list of candidate edges for duplicates. | |
| 183 | 3166 | if (!parallel && added_pairs.contains(endpoints)) |
| 184 | 0 | continue; |
| 185 | ||
| 186 | 3166 | double degree = directed ? attach_point.inDegree() : attach_point.degree(); |
| 187 | ||
| 188 | // subtract 1 from numVertices because we don't want to count newVertex | |
| 189 | // (which has already been added to the graph, but not to vertex_index) | |
| 190 | 3166 | double attach_prob = (degree + 1) / (mGraph.numEdges() + mGraph.numVertices() - 1); |
| 191 | 3166 | if (attach_prob >= mRandom.nextDouble()) |
| 192 | 100 | created_edge = true; |
| 193 | } | |
| 194 | 3166 | while (!created_edge); |
| 195 | ||
| 196 | Edge to_add; | |
| 197 | ||
| 198 | 100 | if (directed) |
| 199 | { | |
| 200 | 0 | to_add = new DirectedSparseEdge(newVertex, attach_point); |
| 201 | 0 | added_pairs.add(endpoints); |
| 202 | } | |
| 203 | else | |
| 204 | { | |
| 205 | 100 | to_add = new UndirectedSparseEdge(newVertex, attach_point); |
| 206 | 100 | added_pairs.add(endpoints); |
| 207 | 100 | added_pairs.add(new Pair(attach_point, newVertex)); |
| 208 | } | |
| 209 | ||
| 210 | 100 | return to_add; |
| 211 | } | |
| 212 | ||
| 213 | public void evolveGraph(int numTimeSteps) { | |
| 214 | ||
| 215 | 110 | for (int i = 0; i < numTimeSteps; i++) { |
| 216 | 100 | evolveGraph(); |
| 217 | 100 | mElapsedTimeSteps++; |
| 218 | } | |
| 219 | 10 | } |
| 220 | ||
| 221 | private void evolveGraph() | |
| 222 | { | |
| 223 | 100 | Set preexistingNodes = mGraph.getVertices(); |
| 224 | Vertex newVertex; | |
| 225 | 100 | if (directed) |
| 226 | 0 | newVertex = new DirectedSparseVertex(); |
| 227 | else | |
| 228 | 100 | newVertex = new UndirectedSparseVertex(); |
| 229 | 100 | mGraph.addVertex(newVertex); |
| 230 | ||
| 231 | // generate and store the new edges; don't add them to the graph | |
| 232 | // yet because we don't want to bias the degree calculations | |
| 233 | // (all new edges in a timestep should be added in parallel) | |
| 234 | 100 | List edges = new LinkedList(); |
| 235 | 100 | HashSet added_pairs = new HashSet(mNumEdgesToAttachPerStep*3); |
| 236 | 200 | for (int i = 0; i < mNumEdgesToAttachPerStep; i++) |
| 237 | 100 | edges.add(createRandomEdge(preexistingNodes, newVertex, added_pairs)); |
| 238 | ||
| 239 | // add edges to graph, now that we have them all | |
| 240 | 100 | for (Iterator iter = edges.iterator(); iter.hasNext(); ) |
| 241 | 100 | mGraph.addEdge((Edge)iter.next()); |
| 242 | ||
| 243 | // now that we're done attaching edges to this new vertex, | |
| 244 | // add it to the index | |
| 245 | 100 | vertex_index.add(newVertex); |
| 246 | 100 | index_vertex.put(newVertex, new Integer(vertex_index.size() - 1)); |
| 247 | 100 | } |
| 248 | ||
| 249 | public int getIndex(Vertex v) | |
| 250 | { | |
| 251 | 0 | return ((Integer)index_vertex.get(v)).intValue(); |
| 252 | } | |
| 253 | ||
| 254 | public int getNumElapsedTimeSteps() { | |
| 255 | 0 | return mElapsedTimeSteps; |
| 256 | } | |
| 257 | ||
| 258 | public ArchetypeGraph generateGraph() { | |
| 259 | 10 | return mGraph; |
| 260 | } | |
| 261 | ||
| 262 | public void reset() { | |
| 263 | 0 | initialize(); |
| 264 | 0 | } |
| 265 | } |
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this report was generated by version 1.0.5 of jcoverage. |
copyright © 2003, jcoverage ltd. all rights reserved. |