Github user tillrohrmann commented on a diff in the pull request:
https://github.com/apache/flink/pull/430#discussion_r25415850
 Diff: docs/gelly_guide.md 
@@ 0,0 +1,425 @@
+
+title: "Gelly: Flink Graph API"
+
+<!
+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/LICENSE2.0
+
+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.
+>
+
+* This will be replaced by the TOC
+{:toc}
+
+<a href="#top"></a>
+
+Introduction
+
+
+Gelly is a Java Graph API for Flink. It contains a set of methods and utilities which
aim to simplify the development of graph analysis applications in Flink. In Gelly, graphs
can be transformed and modified using highlevel functions similar to the ones provided by
the batch processing API. Gelly provides methods to create, transform and modify graphs, as
well as a library of graph algorithms.
+
+Using Gelly
+
+
+Gelly is currently part of the *staging* Maven project. All relevant classes are located
in the *org.apache.flink.graph* package.
+
+Add the following dependency to your `pom.xml` to use Gelly.
+
+~~~xml
+<dependency>
+ <groupId>org.apache.flink</groupId>
+ <artifactId>flinkgelly</artifactId>
+ <version>{{site.FLINK_VERSION_SHORT}}</version>
+</dependency>
+~~~
+
+The remaining sections provide a description of available methods and present several
examples of how to use Gelly and how to mix it with the Flink Java API. After reading this
guide, you might also want to check the {% gh_link /flinkstaging/flinkgelly/src/main/java/org/apache/flink/graph/example/
"Gelly examples" %}.
+
+Graph Representation
+
+
+In Gelly, a `Graph` is represented by a `DataSet` of vertices and a `DataSet` of edges.
+
+The `Graph` nodes are represented by the `Vertex` type. A `Vertex` is defined by a unique
ID and a value. `Vertex` IDs should implement the `Comparable` interface. Vertices without
value can be represented by setting the value type to `NullValue`.
+
+{% highlight java %}
+// create a new vertex with a Long ID and a String value
+Vertex<Long, String> v = new Vertex<Long, String>(1L, "foo");
+
+// create a new vertex with a Long ID and no value
+Vertex<Long, NullValue> v = new Vertex<Long, NullValue>(1L, NullValue.getInstance());
+{% endhighlight %}
+
+The graph edges are represented by the `Edge` type. An `Edge` is defined by a source
ID (the ID of the source `Vertex`), a target ID (the ID of the target `Vertex`) and an optional
value. The source and target IDs should be of the same type as the `Vertex` IDs. Edges with
no value have a `NullValue` value type.
+
+{% highlight java %}
+Edge<Long, Double> e = new Edge<Long, Double>(1L, 2L, 0.5);
+
+// reverse the source and target of this edge
+Edge<Long, Double> reversed = e.reverse();
+
+Double weight = e.getValue(); // weight = 0.5
+{% endhighlight %}
+
+[Back to top](#top)
+
+Graph Creation
+
+
+You can create a `Graph` in the following ways:
+
+* from a `DataSet` of edges and an optional `DataSet` of vertices:
+
+{% highlight java %}
+ExecutionEnvironment env = ExecutionEnvironment.getExecutionEnvironment();
+
+DataSet<Vertex<String, Long>> vertices = ...
+
+DataSet<Edge<String, Double>> edges = ...
+
+Graph<String, Long, Double> graph = Graph.fromDataSet(vertices, edges, env);
+{% endhighlight %}
+
+* from a `DataSet` of `Tuple3` and an optional `DataSet` of `Tuple2`. In this case, Gelly
will convert each `Tuple3` to an `Edge`, where the first field will be the source ID, the
second field will be the target ID and the third field will be the edge value. Equivalently,
each `Tuple2` will be converted to a `Vertex`, where the first field will be the vertex ID
and the second field will be the vertex value:
+
+{% highlight java %}
+ExecutionEnvironment env = ExecutionEnvironment.getExecutionEnvironment();
+
+DataSet<Tuple2<String, Long>> vertexTuples = env.readCsvFile("path/to/vertex/input");
+
+DataSet<Tuple3<String, String, Double>> edgeTuples = env.readCsvFile("path/to/edge/input");
+
+Graph<String, Long, Double> graph = Graph.fromTupleDataSet(vertexTuples, edgeTuples,
env);
+{% endhighlight %}
+
+* from a `Collection` of edges and an optional `Collection` of vertices:
+
+{% highlight java %}
+ExecutionEnvironment env = ExecutionEnvironment.getExecutionEnvironment();
+
+List<Vertex<Long, Long>> vertexList = new ArrayList...
+
+List<Edge<Long, String>> edgeList = new ArrayList...
+
+Graph<Long, Long, String> graph = Graph.fromCollection(vertexList, edgeList, env);
+{% endhighlight %}
+
+If no vertex input is provided during Graph creation, Gelly will automatically produce
the `Vertex` `DataSet` from the edge input. In this case, the created vertices will have no
values. Alternatively, you can provide a `MapFunction` as an argument to the creation method,
in order to initialize the `Vertex` values:
+
+{% highlight java %}
+ExecutionEnvironment env = ExecutionEnvironment.getExecutionEnvironment();
+
+// initialize the vertex value to be equal to the vertex ID
+Graph<Long, Long, String> graph = Graph.fromCollection(edges,
+ new MapFunction<Long, Long>() {
+ public Long map(Long value) {
+ return value;
+ }
+ }, env);
+{% endhighlight %}
+
+[Back to top](#top)
+
+Graph Properties
+
+
+Gelly includes the following methods for retrieving various Graph properties and metrics:
+
+{% highlight java %}
+// get the Vertex DataSet
+DataSet<Vertex<K, VV>> getVertices()
+
+// get the Edge DataSet
+DataSet<Edge<K, EV>> getEdges()
+
+// get the IDs of the vertices as a DataSet
+DataSet<K> getVertexIds()
+
+// get the sourcetarget pairs of the edge IDs as a DataSet
+DataSet<Tuple2<K, K>> getEdgeIds()
+
+// get a DataSet of <vertex ID, indegree> pairs for all vertices
+DataSet<Tuple2<K, Long>> inDegrees()
+
+// get a DataSet of <vertex ID, outdegree> pairs for all vertices
+DataSet<Tuple2<K, Long>> outDegrees()
+
+// get a DataSet of <vertex ID, degree> pairs for all vertices, where degree is
the sum of in and out degrees
+DataSet<Tuple2<K, Long>> getDegrees()
+
+// get the number of vertices
+DataSet<Integer> numberOfVertices()
+
+// get the number of edges
+DataSet<Integer> numberOfEdges()
+
+{% endhighlight %}
+
+[Back to top](#top)
+
+Graph Transformations
+
+
+* <strong>Map</strong>: Gelly provides specialized methods for applying a
map transformation on the vertex values or edge values. `mapVertices` and `mapEdges` return
a new `Graph`, where the IDs of the vertices (or edges) remain unchanged, while the values
are transformed according to the provided userdefined map function. The map functions also
allow changing the type of the vertex or edge values.
+
+{% highlight java %}
+ExecutionEnvironment env = ExecutionEnvironment.getExecutionEnvironment();
+Graph<Long, Long, Long> graph = Graph.fromDataSet(vertices, edges, env);
+
+// increment each vertex value by one
+Graph<Long, Long, Long> updatedGraph = graph.mapVertices(
+ new MapFunction<Vertex<Long, Long>, Long>() {
+ public Long map(Vertex<Long, Long> value) {
+ return value.getValue() + 1;
+ }
+ });
+{% endhighlight %}
+
+* <strong>Filter</strong>: A filter transformation applies a userdefined
filter function on the vertices or edges of the `Graph`. `filterOnEdges` will create a subgraph
of the original graph, keeping only the edges that satisfy the provided predicate. Note that
the vertex dataset will not be modified. Respectively, `filterOnVertices` applies a filter
on the vertices of the graph. Edges whose source and/or target do not satisfy the vertex predicate
are removed from the resulting edge dataset. The `subgraph` method can be used to apply a
filter function to the vertices and the edges at the same time.
+
+{% highlight java %}
+Graph<Long, Long, Long> graph = ...
+
+graph.subgraph(
+ new FilterFunction<Vertex<Long, Long>>() {
+ public boolean filter(Vertex<Long, Long> vertex) {
+ // keep only vertices with positive values
+ return (vertex.getValue() > 0);
+ }
+ },
+ new FilterFunction<Edge<Long, Long>>() {
+ public boolean filter(Edge<Long, Long> edge) {
+ // keep only edges with negative values
+ return (edge.getValue() < 0);
+ }
+ })
+{% endhighlight %}
+
+<p class="textcenter">
+ <img alt="Filter Transformations" width="80%" src="img/gellyfilter.png"/>
+</p>
+
+* <strong>Join</strong>: Gelly provides specialized methods for joining the
vertex and edge datasets with other input datasets. `joinWithVertices` joins the vertices
with a `Tuple2` input data set. The join is performed using the vertex ID and the first field
of the `Tuple2` input as the join keys. The method returns a new `Graph` where the vertex
values have been updated according to the provided a userdefined map function.
+Similarly, an input dataset can be joined with the edges, using one of three methods.
`joinWithEdges` expects an input `DataSet` of `Tuple3` and joins on the composite key of both
source and target vertex IDs. `joinWithEdgesOnSource` expects a `DataSet` of `Tuple2` and
joins on the source key of the edges and the first attribute of the input dataset and `joinWithEdgesOnTarget`
expects a `DataSet` of `Tuple2` and joins on the target key of the edges and the first attribute
of the input dataset. All three methods apply a map function on the edge and the input data
set values.
+Note that if the input dataset contains a key multiple times, all Gelly join methods
will only consider the first value encountered.
+
+{% highlight java %}
+Graph<Long, Double, Double> network = ...
+
+DataSet<Tuple2<Long, Long>> vertexOutDegrees = network.outDegrees();
+
+// assign the transition probabilities as the edge weights
+Graph<Long, Double, Double> networkWithWeights = network.joinWithEdgesOnSource(vertexOutDegrees,
+ new MapFunction<Tuple2<Double, Long>, Double>() {
+ public Double map(Tuple2<Double, Long> value) {
+ return value.f0 / value.f1;
+ }
+ });
+{% endhighlight %}
+
+* <strong>Reverse</strong>: the `reverse()` method returns a new `Graph`
where the direction of all edges has been reversed.
+
+* <strong>Undirected</strong>: In Gelly, a `Graph` is always directed. Undirected
graphs can be represented by adding all oppositedirection edges to a graph. For this purpose,
Gelly provides the `getUndirected()` method.
+
+* <strong>Union</strong>: Gelly's `union()` method performs a union on the
vertex and edges sets of the input graphs. Duplicate vertices are removed from the resulting
`Graph`, while if duplicate edges exists, these will be maintained.
+
+<p class="textcenter">
+ <img alt="Union Transformation" width="50%" src="img/gellyunion.png"/>
+</p>
+
+[Back to top](#top)
+
+Graph Mutations
+
+
+Gelly includes the following methods for adding and removing vertices and edges from
an input `Graph`:
+
+{% highlight java %}
+// adds a Vertex and the given edges to the Graph. If the Vertex already exists, it will
not be added again, but the given edges will.
+Graph<K, VV, EV> addVertex(final Vertex<K, VV> vertex, List<Edge<K,
EV>> edges)
+
+// adds an Edge to the Graph. If the source and target vertices do not exist in the graph,
they will also be added.
+Graph<K, VV, EV> addEdge(Vertex<K, VV> source, Vertex<K, VV> target,
EV edgeValue)
+
+// removes the given Vertex and its edges from the Graph.
+Graph<K, VV, EV> removeVertex(Vertex<K, VV> vertex)
+
+// removes *all* edges that match the given Edge from the Graph.
+Graph<K, VV, EV> removeEdge(Edge<K, EV> edge)
+{% endhighlight %}
+
+Neighborhood Methods
+
+
+Neighborhood methods allow vertices to perform an aggregation on their firsthop neighborhood.
+
+`reduceOnEdges()` can be used to compute an aggregation on the neighboring edges of a
vertex, while `reduceOnNeighbors()` has access on both the neighboring edges and vertices.
The neighborhood scope is defined by the `EdgeDirection` parameter, which takes the values
`IN`, `OUT` or `ALL`. `IN` will gather all incoming edges (neighbors) of a vertex, `OUT`
will gather all outgoing edges (neighbors), while `ALL` will gather all edges (neighbors).
+
+For example, assume that you want to select the minimum weight of all outedges for each
vertex in the following graph:
+
+<p class="textcenter">
+ <img alt="reduceOnEdges Example" width="50%" src="img/gellyexamplegraph.png"/>
+</p>
+
+The following code will collect the outedges for each vertex and apply the `SelectMinWeight()`
userdefined function on each of the resulting neighborhoods:
+
+{% highlight java %}
+Graph<Long, Long, Double> graph = ...
+
+DataSet<Tuple2<Long, Double>> minWeights = graph.reduceOnEdges(
+ new SelectMinWeight(), EdgeDirection.OUT);
+
+// userdefined function to select the minimum weight
+static final class SelectMinWeight implements EdgesFunction<Long, Double, Tuple2<Long,
Double>> {
+
+ public Tuple2<Long, Double> iterateEdges(Iterable<Tuple2<Long, Edge<Long,
Double>>> edges) {
+
+ long minWeight = Double.MAX_VALUE;
+ long vertexId = 1;
+
+ for (Tuple2<Long, Edge<Long, Double>> edge: edges) {
+ if (edge.f1.getValue() < weight) {
+ weight = edge.f1.getValue();
+ vertexId = edge.f0;
+ }
+ return new Tuple2<Long, Double>(vertexId, minWeight);
+ }
+}
+{% endhighlight %}
+
+<p class="textcenter">
+ <img alt="reduceOnEdges Example" width="50%" src="img/gellyreduceOnEdges.png"/>
+</p>
+
+Similarly, assume that you would like to compute the sum of the values of all incoming
neighbors, for every vertex. The following code will collect the incoming neighbors for each
vertex and apply the `SumValues()` userdefined function on each neighborhood:
+
+{% highlight java %}
+Graph<Long, Long, Double> graph = ...
+
+DataSet<Tuple2<Long, Long>> verticesWithSum = graph.reduceOnNeighbors(
+ new SumValues(), EdgeDirection.IN);
+
+// userdefined function to sum the neighbor values
+static final class SumValues implements NeighborsFunction<Long, Long, Long, Tuple2<Long,
Long>> {
 End diff 
Shouldn't the third type parameter be a ```Double``` because the edge values are of this
type?

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