@Override
    public void map(IntWritable nid, PersonalizedPageRankNode node, Context context)
        throws IOException, InterruptedException {

      for (int sourceIndex = 0; sourceIndex < sources.size(); sourceIndex++) {
        float p = node.getPageRank(sourceIndex);

        float jump = 0.0f;
        float link = 0.0f;

        // float jump = (float) (Math.log(ALPHA) - Math.log(nodeCnt));
        // IS A SOURCE NODE
        if (sources.get(sourceIndex) == node.getNodeId()) {
          jump = (float) Math.log(ALPHA);
          link =
              (float) Math.log(1.0f - ALPHA)
                  + sumLogProbs(p, (float) (Math.log(missingMass[sourceIndex])));
        } else {
          // NOT A SOURCE NODE
          jump = (float) Math.log(0);
          link = (float) Math.log(1.0f - ALPHA) + p;
        }

        p = sumLogProbs(jump, link);
        node.setPageRank(sourceIndex, p);
      }

      context.write(nid, node);
    }
    @Override
    public void reduce(IntWritable nid, Iterable<PersonalizedPageRankNode> values, Context context)
        throws IOException, InterruptedException {
      int massMessages = 0;

      // Remember, PageRank mass is stored as a log prob.
      float[] mass = new float[sources.size()];
      for (int i = 0; i < sources.size(); i++) {
        mass[i] = Float.NEGATIVE_INFINITY;
      }

      for (PersonalizedPageRankNode n : values) {
        if (n.getType() == PersonalizedPageRankNode.Type.Structure) {
          // Simply pass along node structure.
          context.write(nid, n);
        } else {
          // Accumulate PageRank mass contributions.
          for (int j = 0; j < sources.size(); j++) {
            mass[j] = sumLogProbs(mass[j], n.getPageRank(j));
          }
          massMessages++;
        }
      }

      // Emit aggregated results.
      if (massMessages > 0) {
        intermediateMass.setNodeId(nid.get());
        intermediateMass.setType(PersonalizedPageRankNode.Type.Mass);
        for (int i = 0; i < sources.size(); i++) {
          intermediateMass.setPageRank(i, mass[i]);
        }

        context.write(nid, intermediateMass);
      }
    }
    @Override
    public void map(IntWritable nid, PersonalizedPageRankNode node, Context context)
        throws IOException, InterruptedException {
      // Pass along node structure.
      intermediateStructure.setNodeId(node.getNodeId());
      intermediateStructure.setType(PersonalizedPageRankNode.Type.Structure);
      intermediateStructure.setAdjacencyList(node.getAdjacenyList());

      context.write(nid, intermediateStructure);

      int massMessages = 0;

      // Distribute PageRank mass to neighbors (along outgoing edges).
      if (node.getAdjacenyList().size() > 0) {
        // Each neighbor gets an equal share of PageRank mass.
        ArrayListOfIntsWritable list = node.getAdjacenyList();
        float mass[] = new float[sources.size()];
        for (int i = 0; i < sources.size(); i++) {
          mass[i] = node.getPageRank(i) - (float) StrictMath.log(list.size());
        }

        context.getCounter(PageRank.edges).increment(list.size());

        // Iterate over neighbors.
        for (int i = 0; i < list.size(); i++) {
          neighbor.set(list.get(i));
          intermediateMass.setNodeId(list.get(i));
          intermediateMass.setType(PersonalizedPageRankNode.Type.Mass);

          for (int j = 0; j < sources.size(); j++) {
            intermediateMass.setPageRank(j, mass[j]);
          }

          // Emit messages with PageRank mass to neighbors.
          context.write(neighbor, intermediateMass);

          massMessages++;
        }
      }

      // Bookkeeping.
      context.getCounter(PageRank.nodes).increment(1);
      context.getCounter(PageRank.massMessages).increment(massMessages);
    }
    @Override
    public void reduce(
        IntWritable nid, Iterable<PersonalizedPageRankNode> iterable, Context context)
        throws IOException, InterruptedException {
      Iterator<PersonalizedPageRankNode> values = iterable.iterator();

      // Create the node structure that we're going to assemble back together from shuffled pieces.
      PersonalizedPageRankNode node = new PersonalizedPageRankNode();

      node.setType(PersonalizedPageRankNode.Type.Complete);
      node.setNodeId(nid.get());

      int massMessagesReceived = 0;
      int structureReceived = 0;

      float[] mass = new float[sources.size()];
      for (int i = 0; i < sources.size(); i++) {
        mass[i] = Float.NEGATIVE_INFINITY;
      }

      while (values.hasNext()) {
        PersonalizedPageRankNode n = values.next();

        if (n.getType().equals(PersonalizedPageRankNode.Type.Structure)) {
          // This is the structure; update accordingly.
          ArrayListOfIntsWritable list = n.getAdjacenyList();
          structureReceived++;

          node.setAdjacencyList(list);
        } else {
          // This is a message that contains PageRank mass; accumulate.
          for (int i = 0; i < sources.size(); i++) {
            mass[i] = sumLogProbs(mass[i], n.getPageRank(i));
          }
          massMessagesReceived++;
        }
      }

      // Update the final accumulated PageRank mass.
      for (int i = 0; i < sources.size(); i++) {
        node.setPageRank(i, mass[i]);
      }
      context.getCounter(PageRank.massMessagesReceived).increment(massMessagesReceived);

      // Error checking.
      if (structureReceived == 1) {
        // Everything checks out, emit final node structure with updated PageRank value.
        context.write(nid, node);

        // Keep track of total PageRank mass.
        for (int i = 0; i < sources.size(); i++) {
          totalMass[i] = sumLogProbs(totalMass[i], mass[i]);
        }
      } else if (structureReceived == 0) {
        // We get into this situation if there exists an edge pointing to a node which has no
        // corresponding node structure (i.e., PageRank mass was passed to a non-existent node)...
        // log and count but move on.
        context.getCounter(PageRank.missingStructure).increment(1);
        LOG.warn(
            "No structure received for nodeid: " + nid.get() + " mass: " + massMessagesReceived);
        // It's important to note that we don't add the PageRank mass to total... if PageRank mass
        // was sent to a non-existent node, it should simply vanish.
      } else {
        // This shouldn't happen!
        throw new RuntimeException(
            "Multiple structure received for nodeid: "
                + nid.get()
                + " mass: "
                + massMessagesReceived
                + " struct: "
                + structureReceived);
      }
    }