Create Edges from Vertices with Spark

Question

Lets say I have an array of vertices and I want to create edges from them in a way that each vertex connects to the next x vertices. x could have any integer value. Is there a way to do that with Spark?

This is what I have with Scala so far:

//array that holds the edges
    var edges = Array.empty[Edge[Double]]
    for(j <- 0 to vertices.size - 2) {
      for(i <- 1 to x) {
        if((j+i) < vertices.size) {
          //add edge
          edges = edges ++ Array(Edge(vertices(j)._1, vertices(j+i)._1, 1.0))
          //add inverse edge, we want both directions
          edges = edges ++ Array(Edge(vertices(j+i)._1, vertices(j)._1, 1.0))
        }
      }
    }

where vertices variable is an array of (Long, String). But the whole process is of course sequential.

Edit:

For example, if I have vertices as such: Hello, World, and, Planet cosmos. I need the following edges: Hello -> World, World -> Hello, Hello -> and, and -> Hello, Hello -> Planet, Planet -> Hello, World -> and, and -> World, World -> Planet, Planet -> World, World -> cosmos, cosmos -> World, and so on.

Answer 1

Do you mean something like this?

// Add dummy vertices at the end (assumes that you don't use negative ids)
(vertices ++ Array.fill(n)((-1L, null))) 
  .sliding(n + 1) // Slide over n + 1 vertices at the time
  .flatMap(arr => { 
     val (srcId, _) = arr.head // Take first
     // Generate 2n edges
     arr.tail.flatMap{case (dstId, _) => 
       Array(Edge(srcId, dstId, 1.0), Edge(dstId, srcId, 1.0))
     }}.filter(e => e.srcId != -1L & e.dstId != -1L)) // Drop dummies
  .toArray

If you want to run it on a RDD you simply adjust an initial step like this:

import org.apache.spark.mllib.rdd.RDDFunctions._

val nPartitions = vertices.partitions.size - 1

vertices.mapPartitionsWithIndex((i, iter) =>
  if (i == nPartitions) (iter ++ Array.fill(n)((-1L, null))).toIterator
  else iter)

and of course drop toArray. If you want circular connections (tail connected to head) you can replace Array.fill(n)((-1L, null)) with vertices.take(n) and drop filter.

Answer 2

So, I think this will get you, what you want:

First off, I define a little helper function (note that I have set edge data here to the vertex names so it's easier to inspect visually):

def pairwiseEdges(list: List[(Long, String)]): List[Edge[String]] = {
  list match {
    case x :: xs => xs.flatMap(i => List(Edge(x._1, i._1, x._2 + "--" + i._2), Edge(i._1, x._1, i._2 + "--" + x._2))) ++ pairwiseEdges(xs)
    case Nil => List.empty
  }
}

I do a zipWithIndex on your array to get a key, and then convert the array to an RDD:

val vertices = List((1L,"hello"), (2L,"world"), (3L,"and"), (4L, "planet"), (5L,"cosmos")).toArray
val indexedVertices = vertices.zipWithIndex
val rdd = sc.parallelize(indexedVertices)

And then to generate the edges with x=3:

val edges = rdd
  .flatMap{case((vertexId, name), index) => for {i <- 0 to 3; if (index - i) >= 0} yield ((index - i, (vertexId, name)))}
  .groupByKey()
  .flatMap{case(index, iterable) => pairwiseEdges(iterable.toList)}
  .distinct()

EDIT: Rewrote the flatmap and removed the filter as suggested by @zero323 in comments.

This will generate the following output:

Edge(1,2,hello--world))
Edge(1,3,hello--and))
Edge(1,4,hello--planet)

Edge(2,1,world--hello)
Edge(2,3,world--and)
Edge(2,4,world--planet)
Edge(2,5,world--cosmos)

Edge(3,1,and--hello)
Edge(3,2,and--world)
Edge(3,4,and--planet)
Edge(3,5,and--cosmos)

Edge(4,1,planet--hello)
Edge(4,2,planet--world)
Edge(4,3,planet--and)
Edge(4,5,planet--cosmos)

Edge(5,2,cosmos--world)
Edge(5,3,cosmos--and)
Edge(5,4,cosmos--planet)