spark-instrumented-optimizer/docs/graphx-programming-guide.md

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global	GraphX Programming Guide

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Overview

GraphX is the new (alpha) Spark API for graphs and graph-parallel computation. At a high-level, GraphX extends the Spark RDD by introducing the Resilient Distributed property Graph (RDG): a directed multigraph with properties attached to each vertex and edge. To support graph computation, GraphX exposes a set of fundamental operators (e.g., subgraph, joinVertices, and mapReduceTriplets) as well as an optimized variant of the Pregel API. In addition, GraphX includes a growing collection of graph algorithms and builders to simplify graph analytics tasks.

Background on Graph-Parallel Computation

From social networks to language modeling, the growing scale and importance of graph data has driven the development of numerous new graph-parallel systems (e.g., Giraph and GraphLab). By restricting the types of computation that can be expressed and introducing new techniques to partition and distribute graphs, these systems can efficiently execute sophisticated graph algorithms orders of magnitude faster than more general data-parallel systems.

However, the same restrictions that enable these substantial performance gains also make it difficult to express many of the important stages in a typical graph-analytics pipeline: constructing the graph, modifying its structure, or expressing computation that spans multiple graphs. As a consequence, existing graph analytics pipelines compose graph-parallel and data-parallel systems, leading to extensive data movement and duplication and a complicated programming model.

The goal of the GraphX project is to unify graph-parallel and data-parallel computation in one system with a single composable API. The GraphX API enables users to view data both as a graph and as collections (i.e., RDDs) without data movement or duplication. By incorporating recent advances in graph-parallel systems, GraphX is able to optimize the execution of graph operations.

GraphX Replaces the Spark Bagel API

Prior to the release of GraphX, graph computation in Spark was expressed using Bagel, an implementation of Pregel. GraphX improves upon Bagel by exposing a richer property graph API, a more streamlined version of the Pregel abstraction, and system optimizations to improve performance and reduce memory overhead. While we plan to eventually deprecate Bagel, we will continue to support the Bagel API and Bagel programming guide. However, we encourage Bagel users to explore the new GraphX API and comment on issues that may complicate the transition from Bagel.

Getting Started

To get started you first need to import Spark and GraphX into your project, as follows:

{% highlight scala %} import org.apache.spark._ import org.apache.spark.graphx._ // To make some of the examples work we will also need RDD import org.apache.spark.rdd.RDD {% endhighlight %}

If you are not using the Spark shell you will also need a SparkContext. To learn more about getting started with Spark refer to the Spark Quick Start Guide.

The Property Graph

The property graph is a directed multigraph with user defined objects attached to each vertex and edge. A directed multigraph is a directed graph with potentially multiple parallel edges sharing the same source and destination vertex. The ability to support parallel edges simplifies modeling scenarios where there can be multiple relationships (e.g., co-worker and friend) between the same vertices. Each vertex is keyed by a unique 64-bit long identifier (VertexId). Similarly, edges have corresponding source and destination vertex identifiers. GraphX does not impose any ordering or constraints on the vertex identifiers. The property graph is parameterized over the vertex VD and edge ED types. These are the types of the objects associated with each vertex and edge respectively.

GraphX optimizes the representation of VD and ED when they are plain old data-types (e.g., int, double, etc...) reducing the in memory footprint.

In some cases we may wish to have vertices with different property types in the same graph. This can be accomplished through inheritance. For example to model users and products as a bipartite graph we might do the following:

{% highlight scala %} class VertexProperty() case class UserProperty(val name: String) extends VertexProperty case class ProductProperty(val name: String, val price: Double) extends VertexProperty // The graph might then have the type: var graph: Graph[VertexProperty, String] = null {% endhighlight %}

Like RDDs, property graphs are immutable, distributed, and fault-tolerant. Changes to the values or structure of the graph are accomplished by producing a new graph with the desired changes. The graph is partitioned across the workers using a range of vertex-partitioning heuristics. As with RDDs, each partition of the graph can be recreated on a different machine in the event of a failure.

Logically the property graph corresponds to a pair of typed collections (RDDs) encoding the properties for each vertex and edge. As a consequence, the graph class contains members to access the vertices and edges of the graph:

{% highlight scala %} val vertices: VertexRDD[VD] val edges: EdgeRDD[ED] {% endhighlight %}

The classes VertexRDD[VD] and EdgeRDD[ED] extend and are optimized versions of RDD[(VertexId, VD)] and RDD[Edge[ED]] respectively. Both VertexRDD[VD] and EdgeRDD[ED] provide additional functionality built around graph computation and leverage internal optimizations. We discuss the VertexRDD and EdgeRDD API in greater detail in the section on vertex and edge RDDs but for now they can be thought of as simply RDDs of the form: RDD[(VertexId, VD)] and RDD[Edge[ED]].

Example Property Graph

Suppose we want to construct a property graph consisting of the various collaborators on the GraphX project. The vertex property might contain the username and occupation. We could annotate edges with a string describing the relationships between collaborators:

The resulting graph would have the type signature:

{% highlight scala %} val userGraph: Graph[(String, String), String] {% endhighlight %}

There are numerous ways to construct a property graph from raw files, RDDs, and even synthetic generators and these are discussed in more detail in the section on graph builders. Probably the most general method is to use the Graph object. For example the following code constructs a graph from a collection of RDDs:

{% highlight scala %} // Assume the SparkContext has already been constructed val sc: SparkContext // Create an RDD for the vertices val users: RDD[(VertexID, (String, String))] = sc.parallelize(Array((3L, ("rxin", "student")), (7L, ("jgonzal", "postdoc")), (5L, ("franklin", "prof")), (2L, ("istoica", "prof")))) // Create an RDD for edges val relationships: RDD[Edge[String]] = sc.parallelize(Array(Edge(3L, 7L, "collab"), Edge(5L, 3L, "advisor"), Edge(2L, 5L, "colleague"), Edge(5L, 7L, "pi"))) // Define a default user in case there are relationship with missing user val defaultUser = ("John Doe", "Missing") // Build the initial Graph val graph = Graph(users, relationships, defaultUser) {% endhighlight %}

In the above example we make use of the Edge case class. Edges have a srcId and a dstId corresponding to the source and destination vertex identifiers. In addition, the Edge class contains the attr member which contains the edge property.

We can deconstruct a graph into the respective vertex and edge views by using the graph.vertices and graph.edges members respectively.

{% highlight scala %} val graph: Graph[(String, String), String] // Constructed from above // Count all users which are postdocs graph.vertices.filter { case (id, (name, pos)) => pos == "postdoc" }.count // Count all the edges where src > dst graph.edges.filter(e => e.srcId > e.dstId).count {% endhighlight %}

Note that graph.vertices returns an VertexRDD[(String, String)] which extends RDD[(VertexId, (String, String))] and so we use the scala case expression to deconstruct the tuple. On the other hand, graph.edges returns an EdgeRDD containing Edge[String] objects. We could have also used the case class type constructor as in the following: {% highlight scala %} graph.edges.filter { case Edge(src, dst, prop) => src > dst }.count {% endhighlight %}

In addition to the vertex and edge views of the property graph, GraphX also exposes a triplet view. The triplet view logically joins the vertex and edge properties yielding an RDD[EdgeTriplet[VD, ED]] containing instances of the EdgeTriplet class. This join can be expressed in the following SQL expression:

{% highlight sql %} SELECT src.id, dst.id, src.attr, e.attr, dst.attr FROM edges AS e LEFT JOIN vertices AS src, vertices AS dst ON e.srcId = src.Id AND e.dstId = dst.Id {% endhighlight %}

or graphically as:

The EdgeTriplet class extends the Edge class by adding the srcAttr and dstAttr members which contain the source and destination properties respectively. We can use the triplet view of a graph to render a collection of strings describing relationships between users.

{% highlight scala %} val graph: Graph[(String, String), String] // Constructed from above // Use the triplets view to create an RDD of facts. val facts: RDD[String] = graph.triplets.map(triplet => triplet.srcAttr._1 + " is the " + triplet.attr + " of " + triplet.dstAttr.1) facts.collect.foreach(println()) {% endhighlight %}

Graph Operators

Just as RDDs have basic operations like map, filter, and reduceByKey, property graphs also have a collection of basic operators that take user defined functions and produce new graphs with transformed properties and structure. The core operators that have optimized implementations are defined in Graph and convenient operators that are expressed as a compositions of the core operators are defined in GraphOps. However, thanks to Scala implicits the operators in GraphOps are automatically available as members of Graph. For example, we can compute the in-degree of each vertex (defined in GraphOps) by the following:

{% highlight scala %} val graph: Graph[(String, String), String] // Use the implicit GraphOps.inDegrees operator val indDegrees: VertexRDD[Int] = graph.inDegrees {% endhighlight %}

The reason for differentiating between core graph operations and GraphOps is to be able to support different graph representations in the future. Each graph representation must provide implementations of the core operations and reuse many of the useful operations defined in GraphOps.

Property Operators

In direct analogy to the RDD map operator, the property graph contains the following:

{% highlight scala %} def mapVertices[VD2](map: (VertexID, VD) => VD2): Graph[VD2, ED] def mapEdges[ED2](map: Edge[ED] => ED2): Graph[VD, ED2] def mapTriplets[ED2](map: EdgeTriplet[VD, ED] => ED2): Graph[VD, ED2] {% endhighlight %}

Each of these operators yields a new graph with the vertex or edge properties modified by the user defined map function.

Note that in all cases the graph structure is unaffected. This is a key feature of these operators which allows the resulting graph to reuse the structural indices of the original graph. The following snippets are logically equivalent, but the first one does not preserve the structural indices and would not benefit from the GraphX system optimizations: {% highlight scala %} val newVertices = graph.vertices.map { case (id, attr) => (id, mapUdf(id, attr)) } val newGraph = Graph(newVertices, graph.edges) {% endhighlight %} Instead, use mapVertices to preserve the indices: {% highlight scala %} val newGraph = graph.mapVertices((id, attr) => mapUdf(id, attr)) {% endhighlight %}

These operators are often used to initialize the graph for a particular computation or project away unnecessary properties. For example, given a graph with the out-degrees as the vertex properties (we describe how to construct such a graph later), we initialize it for PageRank:

{% highlight scala %} // Given a graph where the vertex property is the out-degree val inputGraph: Graph[Int, String] = graph.outerJoinVertices(graph.outDegrees)((vid, _, degOpt) => degOpt.getOrElse(0)) // Construct a graph where each edge contains the weight // and each vertex is the initial PageRank val outputGraph: Graph[Double, Double] = inputGraph.mapTriplets(triplet => 1.0 / triplet.srcAttr).mapVertices((id, _) => 1.0) {% endhighlight %}

Structural Operators

Currently GraphX supports only a simple set of commonly used structural operators and we expect to add more in the future. The following is a list of the basic structural operators.

{% highlight scala %} def reverse: Graph[VD, ED] def subgraph(epred: EdgeTriplet[VD,ED] => Boolean, vpred: (VertexID, VD) => Boolean): Graph[VD, ED] def mask[VD2, ED2](other: Graph[VD2, ED2]): Graph[VD, ED] def groupEdges(merge: (ED, ED) => ED): Graph[VD,ED] {% endhighlight %}

The reverse operator returns a new graph with all the edge directions reversed. This can be useful when, for example, trying to compute the inverse PageRank. Because the reverse operation does not modify vertex or edge properties or change the number of edges, it can be implemented efficiently without data-movement or duplication.

The subgraph operator takes vertex and edge predicates and returns the graph containing only the vertices that satisfy the vertex predicate (evaluate to true) and edges that satisfy the edge predicate and connect vertices that satisfy the vertex predicate. The subgraph operator can be used in number of situations to restrict the graph to the vertices and edges of interest or eliminate broken links. For example in the following code we remove broken links:

{% highlight scala %} // Create an RDD for the vertices val users: RDD[(VertexID, (String, String))] = sc.parallelize(Array((3L, ("rxin", "student")), (7L, ("jgonzal", "postdoc")), (5L, ("franklin", "prof")), (2L, ("istoica", "prof")), (4L, ("peter", "student")))) // Create an RDD for edges val relationships: RDD[Edge[String]] = sc.parallelize(Array(Edge(3L, 7L, "collab"), Edge(5L, 3L, "advisor"), Edge(2L, 5L, "colleague"), Edge(5L, 7L, "pi"), Edge(4L, 0L, "student"), Edge(5L, 0L, "colleague"))) // Define a default user in case there are relationship with missing user val defaultUser = ("John Doe", "Missing") // Build the initial Graph val graph = Graph(users, relationships, defaultUser) // Notice that there is a user 0 (for which we have no information) connecting users // 4 (peter) and 5 (franklin). graph.triplets.map( triplet => triplet.srcAttr._1 + " is the " + triplet.attr + " of " + triplet.dstAttr.1 ).collect.foreach(println()) // Remove missing vertices as well as the edges to connected to them val validGraph = graph.subgraph(vpred = (id, attr) => attr.2 != "Missing") // The valid subgraph will disconnect users 4 and 5 by removing user 0 validGraph.vertices.collect.foreach(println()) validGraph.triplets.map( triplet => triplet.srcAttr._1 + " is the " + triplet.attr + " of " + triplet.dstAttr.1 ).collect.foreach(println()) {% endhighlight %}

Note in the above example only the vertex predicate is provided. The subgraph operator defaults to true if the vertex or edge predicates are not provided.

The mask operator also constructs a subgraph by returning a graph that contains the vertices and edges that are also found in the input graph. This can be used in conjunction with the subgraph operator to restrict a graph based on the properties in another related graph. For example, we might run connected components using the graph with missing vertices and then restrict the answer to the valid subgraph.

{% highlight scala %} // Run Connected Components val ccGraph = graph.connectedComponents() // No longer contains missing field // Remove missing vertices as well as the edges to connected to them val validGraph = graph.subgraph(vpred = (id, attr) => attr._2 != "Missing") // Restrict the answer to the valid subgraph val validCCGraph = ccGraph.mask(validGraph) {% endhighlight %}

The groupEdges operator merges parallel edges (i.e., duplicate edges between pairs of vertices) in the multigraph. In many numerical applications, parallel edges can be added (their weights combined) into a single edge thereby reducing the size of the graph.

Join Operators

In many cases it is necessary to join data from external collections (RDDs) with graphs. For example, we might have extra user properties that we want to merge with an existing graph or we might want to pull vertex properties from one graph into another. These tasks can be accomplished using the join operators. Below we list the key join operators:

{% highlight scala %} def joinVertices[U](table: RDD[(VertexID, U)])(map: (VertexID, VD, U) => VD) : Graph[VD, ED] def outerJoinVertices[U, VD2](table: RDD[(VertexID, U)])(map: (VertexID, VD, Option[U]) => VD2) : Graph[VD2, ED] {% endhighlight %}

The joinVertices operator joins the vertices with the input RDD and returns a new graph with the vertex properties obtained by applying the user defined map function to the result of the joined vertices. Vertices without a matching value in the RDD retain their original value.

Note that if the RDD contains more than one value for a given vertex only one will be used. It is therefore recommended that the input RDD be first made unique using the following which will also pre-index the resulting values to substantially accelerate the subsequent join. {% highlight scala %} val nonUniqueCosts: RDD[(VertexId, Double)] val uniqueCosts: VertexRDD[Double] = graph.vertices.aggregateUsingIndex(nonUnique, (a,b) => a + b) val joinedGraph = graph.joinVertices(uniqueCosts)( (id, oldCost, extraCost) => oldCost + extraCost) {% endhighlight %}

The more general outerJoinVertices behaves similarly to joinVertices except that the user defined map function is applied to all vertices and can change the vertex property type. Because not all vertices may have a matching value in the input RDD the map function takes an Option type. For example, we can setup a graph for PageRank by initializing vertex properties with their outDegree.

{% highlight scala %} val outDegrees: VertexRDD[Int] = graph.outDegrees val degreeGraph = graph.outerJoinVertices(outDegrees) { (id, oldAttr, outDegOpt) => outDegOpt match { case Some(outDeg) => outDeg case None => 0 // No outDegree means zero outDegree } } {% endhighlight %}

You may have noticed the multiple parameter lists (e.g., f(a)(b)) curried function pattern used in the above examples. While we could have equally written f(a)(b) as f(a,b) this would mean that type inference on b would not depend on a. As a consequence, the user would need to provide type annotation for the user defined function: {% highlight scala %} val joinedGraph = graph.joinVertices(uniqueCosts, (id: VertexId, oldCost: Double, extraCost: Double) => oldCost + extraCost) {% endhighlight %}

Neighborhood Aggregation

A key part of graph computation is aggregating information about the neighborhood of each vertex. For example we might want to know the number of followers each user has or the average age of the the followers of each user. Many iterative graph algorithms (e.g., PageRank, Shortest Path, and connected components) repeatedly aggregate properties of neighboring vertices (e.g., current PageRank Value, shortest path to the source, and smallest reachable vertex id).

Map Reduce Triplets (mapReduceTriplets)

The core (heavily optimized) aggregation primitive in GraphX is the mapReduceTriplets operator:

{% highlight scala %} def mapReduceTriplets[A]( map: EdgeTriplet[VD, ED] => Iterator[(VertexID, A)], reduce: (A, A) => A) : VertexRDD[A] {% endhighlight %}

The mapReduceTriplets operator takes a user defined map function which is applied to each triplet and can yield messages destined to either (none or both) vertices in the triplet. To facilitate optimized pre-aggregation, we currently only support messages destined to the source or destination vertex of the triplet. The user defined reduce function combines the messages destined to each vertex. The mapReduceTriplets operator returns a VertexRDD[A] containing the aggregate message (of type A) destined to each vertex. Vertices that do not receive a message are not included in the returned VertexRDD.

Note that mapReduceTriplets takes an additional optional activeSet (see API docs) which restricts the map phase to edges adjacent to the vertices in the provided VertexRDD:

{% highlight scala %} activeSetOpt: Option[(VertexRDD[_], EdgeDirection)] = None {% endhighlight %}

The EdgeDirection specifies which edges adjacent to the vertex set are included in the map phase. If the direction is In, mapFunc will only be run only on edges with destination in the active set. If the direction is Out, mapFunc will only be run only on edges originating from vertices in the active set. If the direction is Either, mapFunc will be run only on edges with either vertex in the active set. If the direction is Both, mapFunc will be run only on edges with both vertices in the active set. The active set must be derived from the set of vertices in the graph. Restricting computation to triplets adjacent to a subset of the vertices is often necessary in incremental iterative computation and is a key part of the GraphX implementation of Pregel.

In the following example we use the mapReduceTriplets operator to compute the average age of the more senior followers of each user.

{% highlight scala %} // Import random graph generation library import org.apache.spark.graphx.util.GraphGenerators // Create a graph with "age" as the vertex property. Here we use a random graph for simplicity. val graph: Graph[Double, Int] = GraphGenerators.logNormalGraph(sc, numVertices = 100).mapVertices( (id, _) => id.toDouble ) // Compute the number of older followers and their total age val olderFollowers: VertexRDD[(Int, Double)] = graph.mapReduceTriplets[(Int, Double)]( triplet => { // Map Function if (triplet.srcAttr > triplet.dstAttr) { // Send message to destination vertex containing counter and age Iterator((triplet.dstId, (1, triplet.srcAttr))) } else { // Don't send a message for this triplet Iterator.empty } }, // Add counter and age (a, b) => (a._1 + b._1, a._2 + b.2) // Reduce Function ) // Divide total age by number of older followers to get average age of older followers val avgAgeOfOlderFollowers: VertexRDD[Double] = olderFollowers.mapValues( (id, value) => value match { case (count, totalAge) => totalAge / count } ) // Display the results avgAgeOfOlderFollowers.collect.foreach(println()) {% endhighlight %}

Note that the mapReduceTriplets operation performs optimally when the messages (and their sums) are constant sized (e.g., floats and addition instead of lists and concatenation). More precisely, the result of mapReduceTriplets should ideally be sub-linear in the degree of each vertex.

Computing Degree Information

A common aggregation task is computing the degree of each vertex: the number of edges adjacent to each vertex. In the context of directed graphs it often necessary to know the in-degree, out- degree, and the total degree of each vertex. The GraphOps class contains a collection of operators to compute the degrees of each vertex. For example in the following we compute the max in, out, and total degrees:

{% highlight scala %} // Define a reduce operation to compute the highest degree vertex def max(a: (VertexID, Int), b: (VertexID, Int)): (VertexID, Int) = { if (a._2 > b._2) a else b } // Compute the max degrees val maxInDegree: (VertexID, Int) = graph.inDegrees.reduce(max) val maxOutDegree: (VertexID, Int) = graph.outDegrees.reduce(max) val maxDegrees: (VertexID, Int) = graph.degrees.reduce(max) {% endhighlight %}

Collecting Neighbors

In some cases it may be easier to express computation by collecting neighboring vertices and their attributes at each vertex. This can be easily accomplished using the collectNeighborIds and the collectNeighbors operators.

{% highlight scala %} def collectNeighborIds(edgeDirection: EdgeDirection): VertexRDD[Array[VertexID]] = def collectNeighbors(edgeDirection: EdgeDirection): VertexRDD[ Array[(VertexID, VD)] ] {% endhighlight %}

Note that these operators can be quite costly as they duplicate information and require substantial communication. If possible try expressing the same computation using the mapReduceTriplets operator directly.

Pregel API

Graphs are inherently recursive data-structures as properties of vertices depend on properties of their neighbors which intern depend on properties of their neighbors. As a consequence many important graph algorithms iteratively recompute the properties of each vertex until a fixed-point condition is reached. A range of graph-parallel abstractions have been proposed to express these iterative algorithms. GraphX exposes a Pregel-like operator which is a fusion of the widely used Pregel and GraphLab abstractions.

At a high-level the Pregel operator in GraphX is a bulk-synchronous parallel messaging abstraction constrained to the topology of the graph. The Pregel operator executes in a series of super-steps in which vertices receive the sum of their inbound messages from the previous super- step, compute a new value for the vertex property, and then send messages to neighboring vertices in the next super-step. Unlike Pregel and instead more like GraphLab messages are computed in parallel as a function of the edge triplet and the message computation has access to both the source and destination vertex attributes. Vertices that do not receive a message are skipped within a super- step. The Pregel operators terminates iteration and returns the final graph when there are no messages remaining.

Note, unlike more standard Pregel implementations, vertices in GraphX can only send messages to neighboring vertices and the message construction is done in parallel using a user defined messaging function. These constraints allow additional optimization within GraphX.

The following is type signature of the Pregel operator as well as a sketch of its implementation (note calls to graph.cache have been removed):

{% highlight scala %} def pregel[A] (initialMsg: A, maxIter: Int = Int.MaxValue, activeDir: EdgeDirection = EdgeDirection.Out) (vprog: (VertexID, VD, A) => VD, sendMsg: EdgeTriplet[VD, ED] => Iterator[(VertexID, A)], mergeMsg: (A, A) => A) : Graph[VD, ED] = { // Receive the initial message at each vertex var g = mapVertices( (vid, vdata) => vprog(vid, vdata, initialMsg) ).cache() // compute the messages var messages = g.mapReduceTriplets(sendMsg, mergeMsg) var activeMessages = messages.count() // Loop until no messages remain or maxIterations is achieved var i = 0 while (activeMessages > 0 && i < maxIterations) { // Receive the messages: ----------------------------------------------------------------------- // Run the vertex program on all vertices that receive messages val newVerts = g.vertices.innerJoin(messages)(vprog).cache() // Merge the new vertex values back into the graph g = g.outerJoinVertices(newVerts) { (vid, old, newOpt) => newOpt.getOrElse(old) }.cache() // Send Messages: ------------------------------------------------------------------------------ // Vertices that didn't receive a message above don't appear in newVerts and therefore don't // get to send messages. More precisely the map phase of mapReduceTriplets is only invoked // on edges in the activeDir of vertices in newVerts messages = g.mapReduceTriplets(sendMsg, mergeMsg, Some((newVerts, activeDir))).cache() activeMessages = messages.count() i += 1 } g } {% endhighlight %}

Notice that Pregel takes two argument lists (i.e., graph.pregel(list1)(list2)). The first argument list contains configuration parameters including the initial message, the maximum number of iterations, and the edge direction in which to send messages (by default along out edges). The second argument list contains the user defined functions for receiving messages (the vertex program vprog), computing messages (sendMsg), and combining messages mergeMsg.

We can use the Pregel operator to express computation such as single source shortest path in the following example.

{% highlight scala %} import org.apache.spark.graphx._ // Import random graph generation library import org.apache.spark.graphx.util.GraphGenerators // A graph with edge attributes containing distances val graph: Graph[Int, Double] = GraphGenerators.logNormalGraph(sc, numVertices = 100).mapEdges(e => e.attr.toDouble) val sourceId: VertexID = 42 // The ultimate source // Initialize the graph such that all vertices except the root have distance infinity. val initialGraph = graph.mapVertices((id, _) => if (id == sourceId) 0.0 else Double.PositiveInfinity) val sssp = initialGraph.pregel(Double.PositiveInfinity)( (id, dist, newDist) => math.min(dist, newDist), // Vertex Program triplet => { // Send Message if (triplet.srcAttr + triplet.attr < triplet.dstAttr) { Iterator((triplet.dstId, triplet.srcAttr + triplet.attr)) } else { Iterator.empty } }, (a,b) => math.min(a,b) // Merge Message ) println(sssp.vertices.collect.mkString("\n")) {% endhighlight %}

Graph Builders

GraphLoader.edgeListFile

Graph.apply

Graph.fromEdgeTuples

Graph.fromEdges

Vertex and Edge RDDs

GraphX exposes RDD views of the vertices and edges stored within the graph. However, because GraphX maintains the vertices and edges in optimized data-structures and these data-structures provide additional functionality, the vertices and edges are returned as VertexRDD and EdgeRDD respectively. In this section we review some of the additional useful functionality in these types.

VertexRDDs

The VertexRDD[A] extends the more traditional RDD[(VertexId, A)] but adds the additional constraint that each VertexId occurs only once. Moreover, VertexRDD[A] represents a set of vertices each with an attribute of type A. Internally, this is achieved by storing the vertex attributes in a reusable hash-map data-structure. As a consequence if two VertexRDDs are derived from the same base VertexRDD (e.g., by filter or mapValues) they can be joined in constant time without hash evaluations. To leverage this indexed data-structure, the VertexRDD exposes the following additional functionality:

{% highlight scala %} // Filter the vertex set but preserves the internal index def filter(pred: Tuple2[VertexID, VD] => Boolean): VertexRDD[VD] // Transform the values without changing the ids (preserves the internal index) def mapValues[VD2](map: VD => VD2): VertexRDD[VD2] def mapValues[VD2](map: (VertexID, VD) => VD2): VertexRDD[VD2] // Remove vertices from this set that appear in the other set def diff(other: VertexRDD[VD]): VertexRDD[VD] // Join operators that take advantage of the internal indexing to accelerate joins (substantially) def leftJoin[VD2, VD3](other: RDD[(VertexID, VD2)])(f: (VertexID, VD, Option[VD2]) => VD3): VertexRDD[VD3] def innerJoin[U, VD2](other: RDD[(VertexID, U)])(f: (VertexID, VD, U) => VD2): VertexRDD[VD2] // Use the index on this RDD to accelerate a reduceByKey operation on the input RDD. def aggregateUsingIndex[VD2](other: RDD[(VertexID, VD2)], reduceFunc: (VD2, VD2) => VD2): VertexRDD[VD2] {% endhighlight %}

Notice, for example, how the filter operator returns an VertexRDD. Filter is actually implemented using a BitSet thereby reusing the index and preserving the ability to do fast joins with other VertexRDDs. Likewise, the mapValues operators do not allow the map function to change the VertexId thereby enabling the same HashMap data-structures to be reused. Both the leftJoin and innerJoin are able to identify when joining two VertexRDDs derived from the same HashMap and implement the join by linear scan rather than costly point lookups.

The aggregateUsingIndex operator can be slightly confusing but is also useful for efficient construction of a new VertexRDD from an RDD[(VertexId, A)]. Conceptually, if I have constructed a VertexRDD[B] over a set of vertices, which is a super-set of the vertices in some RDD[(VertexId, A)] then I can reuse the index to both aggregate and then subsequently index the RDD. For example:

{% highlight scala %} val setA: VertexRDD[Int] = VertexRDD(sc.parallelize(0L until 100L).map(id => (id, 1))) val rddB: RDD[(VertexID, Double)] = sc.parallelize(0L until 100L).flatMap(id => List((id, 1.0), (id, 2.0))) // There should be 200 entries in rddB rddB.count val setB: VertexRDD[Double] = setA.aggregateUsingIndex(rddB, _ + _) // There should be 100 entries in setB setB.count // Joining A and B should now be fast! val setC: VertexRDD[Double] = setA.innerJoin(setB)((id, a, b) => a + b) {% endhighlight %}

Optimized Representation

This section should give some intuition about how GraphX works and how that affects the user (e.g., things to worry about.)

Graph Algorithms

GraphX includes a set of graph algorithms in to simplify analytics. The algorithms are contained in the org.apache.spark.graphx.lib package and can be accessed directly as methods on Graph via GraphOps. This section describes the algorithms and how they are used.

PageRank

PageRank measures the importance of each vertex in a graph, assuming an edge from u to v represents an endorsement of v's importance by u. For example, if a Twitter user is followed by many others, the user will be ranked highly.

GraphX comes with static and dynamic implementations of PageRank as methods on the PageRank object. Static PageRank runs for a fixed number of iterations, while dynamic PageRank runs until the ranks converge (i.e., stop changing by more than a specified tolerance). GraphOps allows calling these algorithms directly as methods on Graph.

GraphX also includes an example social network dataset that we can run PageRank on. A set of users is given in graphx/data/users.txt, and a set of relationships between users is given in graphx/data/followers.txt. We compute the PageRank of each user as follows:

{% highlight scala %} // Load the edges as a graph val graph = GraphLoader.edgeListFile(sc, "graphx/data/followers.txt") // Run PageRank val ranks = graph.pageRank(0.0001).vertices // Join the ranks with the usernames val users = sc.textFile("graphx/data/users.txt").map { line => val fields = line.split("\s+") (fields(0).toLong, fields(1)) } val ranksByUsername = users.leftOuterJoin(ranks).map { case (id, (username, rankOpt)) => (username, rankOpt.getOrElse(0.0)) } // Print the result println(ranksByUsername.collect().mkString("\n")) {% endhighlight %}

Connected Components

The connected components algorithm labels each connected component of the graph with the ID of its lowest-numbered vertex. For example, in a social network, connected components can approximate clusters. GraphX contains an implementation of the algorithm in the ConnectedComponents object, and we compute the connected components of the example social network dataset from the PageRank section as follows:

{% highlight scala %} // Load the graph as in the PageRank example val graph = GraphLoader.edgeListFile(sc, "graphx/data/followers.txt") // Find the connected components val cc = graph.connectedComponents().vertices // Join the connected components with the usernames val users = sc.textFile("graphx/data/users.txt").map { line => val fields = line.split("\s+") (fields(0).toLong, fields(1)) } val ccByUsername = users.join(cc).map { case (id, (username, cc)) => (username, cc) } // Print the result println(ccByUsername.collect().mkString("\n")) {% endhighlight %}

Triangle Counting

A vertex is part of a triangle when it has two adjacent vertices with an edge between them. GraphX implements a triangle counting algorithm in the TriangleCount object that determines the number of triangles passing through each vertex, providing a measure of clustering. We compute the triangle count of the social network dataset from the PageRank section. Note that TriangleCount requires the edges to be in canonical orientation (srcId < dstId) and the graph to be partitioned using Graph#partitionBy.

{% highlight scala %} // Load the edges in canonical order and partition the graph for triangle count val graph = GraphLoader.edgeListFile(sc, "graphx/data/followers.txt", true).partitionBy(RandomVertexCut) // Find the triangle count for each vertex val triCounts = graph.triangleCount().vertices // Join the triangle counts with the usernames val users = sc.textFile("graphx/data/users.txt").map { line => val fields = line.split("\s+") (fields(0).toLong, fields(1)) } val triCountByUsername = users.join(triCounts).map { case (id, (username, tc)) => (username, tc) } // Print the result println(triCountByUsername.collect().mkString("\n")) {% endhighlight %}

Examples

Suppose I want to build a graph from some text files, restrict the graph to important relationships and users, run page-rank on the sub-graph, and then finally return attributes associated with the top users. I can do all of this in just a few lines with GraphX:

{% highlight scala %} // Connect to the Spark cluster val sc = new SparkContext("spark://master.amplab.org", "research")

// Load my user data and prase into tuples of user id and attribute list val users = sc.textFile("hdfs://user_attributes.tsv") .map(line => line.split).map( parts => (parts.head, parts.tail) )

// Parse the edge data which is already in userId -> userId format val followerGraph = Graph.textFile(sc, "hdfs://followers.tsv")

// Attach the user attributes val graph = followerGraph.outerJoinVertices(users){ case (uid, deg, Some(attrList)) => attrList // Some users may not have attributes so we set them as empty case (uid, deg, None) => Array.empty[String] }

// Restrict the graph to users which have exactly two attributes val subgraph = graph.subgraph((vid, attr) => attr.size == 2)

// Compute the PageRank val pagerankGraph = Analytics.pagerank(subgraph)

// Get the attributes of the top pagerank users val userInfoWithPageRank = subgraph.outerJoinVertices(pagerankGraph.vertices){ case (uid, attrList, Some(pr)) => (pr, attrList) case (uid, attrList, None) => (pr, attrList) }

println(userInfoWithPageRank.top(5))

{% endhighlight %}