initial version of LPA

A straightforward implementation of LPA algorithm for detecting graph communities using the Pregel framework.  Amongst the growing literature on community detection algorithms in networks, LPA is perhaps the most elementary, and despite its flaws it remains a nice and simple approach.

Author: Ankur Dave <ankurdave@gmail.com>
Author: haroldsultan <haroldsultan@gmail.com>
Author: Harold Sultan <haroldsultan@gmail.com>

Closes #905 from haroldsultan/master and squashes the following commits:

327aee0 [haroldsultan] Merge pull request #2 from ankurdave/label-propagation
227a4d0 [Ankur Dave] Untabify
0ac574c [haroldsultan] Merge pull request #1 from ankurdave/label-propagation
0e24303 [Ankur Dave] Add LabelPropagationSuite
84aa061 [Ankur Dave] LabelPropagation: Fix compile errors and style; rename from LPA
9830342 [Harold Sultan] initial version of LPA

graphx/src/main/scala/org/apache/spark/graphx/lib/LabelPropagation.scala

+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.graphx.lib
+
+import scala.reflect.ClassTag
+import org.apache.spark.graphx._
+
+/** Label Propagation algorithm. */
+object LabelPropagation {
+  /**
+   * Run static Label Propagation for detecting communities in networks.
+   *
+   * Each node in the network is initially assigned to its own community. At every superstep, nodes
+   * send their community affiliation to all neighbors and update their state to the mode community
+   * affiliation of incoming messages.
+   *
+   * LPA is a standard community detection algorithm for graphs. It is very inexpensive
+   * computationally, although (1) convergence is not guaranteed and (2) one can end up with
+   * trivial solutions (all nodes are identified into a single community).
+   *
+   * @tparam ED the edge attribute type (not used in the computation)
+   *
+   * @param graph the graph for which to compute the community affiliation
+   * @param maxSteps the number of supersteps of LPA to be performed. Because this is a static
+   * implementation, the algorithm will run for exactly this many supersteps.
+   *
+   * @return a graph with vertex attributes containing the label of community affiliation
+   */
+  def run[ED: ClassTag](graph: Graph[_, ED], maxSteps: Int): Graph[VertexId, ED] = {
+    val lpaGraph = graph.mapVertices { case (vid, _) => vid }
+    def sendMessage(e: EdgeTriplet[VertexId, ED]) = {
+      Iterator((e.srcId, Map(e.dstAttr -> 1L)), (e.dstId, Map(e.srcAttr -> 1L)))
+    }
+    def mergeMessage(count1: Map[VertexId, Long], count2: Map[VertexId, Long])
+      : Map[VertexId, Long] = {
+      (count1.keySet ++ count2.keySet).map { i =>
+        val count1Val = count1.getOrElse(i, 0L)
+        val count2Val = count2.getOrElse(i, 0L)
+        i -> (count1Val + count2Val)
+      }.toMap
+    }
+    def vertexProgram(vid: VertexId, attr: Long, message: Map[VertexId, Long]) = {
+      if (message.isEmpty) attr else message.maxBy(_._2)._1
+    }
+    val initialMessage = Map[VertexId, Long]()
+    Pregel(lpaGraph, initialMessage, maxIterations = maxSteps)(
+      vprog = vertexProgram,
+      sendMsg = sendMessage,
+      mergeMsg = mergeMessage)
+  }
+}

graphx/src/test/scala/org/apache/spark/graphx/lib/LabelPropagationSuite.scala

+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.graphx.lib
+
+import org.scalatest.FunSuite
+
+import org.apache.spark.graphx._
+
+class LabelPropagationSuite extends FunSuite with LocalSparkContext {
+  test("Label Propagation") {
+    withSpark { sc =>
+      // Construct a graph with two cliques connected by a single edge
+      val n = 5
+      val clique1 = for (u <- 0L until n; v <- 0L until n) yield Edge(u, v, 1)
+      val clique2 = for (u <- 0L to n; v <- 0L to n) yield Edge(u + n, v + n, 1)
+      val twoCliques = sc.parallelize(clique1 ++ clique2 :+ Edge(0L, n, 1))
+      val graph = Graph.fromEdges(twoCliques, 1)
+      // Run label propagation
+      val labels = LabelPropagation.run(graph, n * 4).cache()
+
+      // All vertices within a clique should have the same label
+      val clique1Labels = labels.vertices.filter(_._1 < n).map(_._2).collect.toArray
+      assert(clique1Labels.forall(_ == clique1Labels(0)))
+      val clique2Labels = labels.vertices.filter(_._1 >= n).map(_._2).collect.toArray
+      assert(clique2Labels.forall(_ == clique2Labels(0)))
+      // The two cliques should have different labels
+      assert(clique1Labels(0) != clique2Labels(0))
+    }
+  }
+}