Multigraph

About

This library provides:

An implementation of a graph datastructure, Graph, designed for both directed and undirected graphs. The API supports undirected graphs, but I'm still getting the tests updated to cover properties of undirected graphs.
A priority queue implementation PriorityQueue, oriented towards graphs (it prioritizes lower integer values over high), it is the fastest priority queue I know of which allows arbitrary priorities, and is more or less at parity with pqueue3 from the pqueue library, which supports priorities from 0 to 65535.
An idiomatic Elixir API for creating, modifying, and querying its graph structure. Creating and modifying a graph can be done in a single pipeline, and all queries take a Graph as their first parameter (one of my complaints with :digraph is that there is some inconsistency with the API between :digraph and :digraph_utils for no apparent reason).
Two "Reducer" implementations for mapping/reducing over a graph. I am trying to figure out the best way to make these extendable and part of the API, so that you can drop in your own shortest path algorithms, etc - but I have yet to come up with an approach that feels good on that front.
A Serializer behaviour, for defining custom serialization of graphs, with a Graphviz DOT format serializer provided out of the box.

It is backed by a large suite of tests, including several QuickCheck properties for the graph model. Its API shares some similarity with :digraph, but diverges in favor of a more idiomatic Elixir interface. In addition, over time I'm adding new functions to query the graph in ways not previously supported via :digraph, and introducing support for classifying a graph as undirected if so desired, so that queries over such graphs become easier.

If you are interested in reading more about how you can make use of libgraph, there is an excellent blog post written by Tony Hammond which is a very helpful walkthrough of the library and what can be built with it.

Installation

If available in Hex, the package can be installed by adding multigraph to your list of dependencies in mix.exs:

def deps do
  [{:multigraph, "~> 0.16.1-mg.2"}]
end

Multigraphs

Libgraph supports multigraphs — graphs where multiple edges with different labels can exist between the same pair of vertices. When multigraph: true is enabled, an edge adjacency index is maintained that allows O(1) lookup of edges by partition key, avoiding full edge scans.

Creating a multigraph

g =
  Graph.new(multigraph: true)
  |> Graph.add_edges([
    {:a, :b, label: :uses},
    {:a, :b, label: :contains},
    {:b, :c, label: :uses},
    {:b, :c, label: :owns, weight: 3}
  ])

Querying by partition

By default, edges are partitioned by their label (via Graph.Utils.by_edge_label/1). You can query edges belonging to a specific partition:

# Get only :uses edges
Graph.edges(g, by: :uses)
#=> [%Graph.Edge{v1: :a, v2: :b, label: :uses}, %Graph.Edge{v1: :b, v2: :c, label: :uses}]

# Get out edges from :a with label :contains
Graph.out_edges(g, :a, by: :contains)
#=> [%Graph.Edge{v1: :a, v2: :b, label: :contains}]

# Filter edges with a predicate
Graph.edges(g, where: fn edge -> edge.weight > 2 end)
#=> [%Graph.Edge{v1: :b, v2: :c, label: :owns, weight: 3}]

Custom partition functions

You can provide a custom partition_by function to control how edges are indexed:

g = Graph.new(multigraph: true, partition_by: fn edge -> [edge.weight] end)
|> Graph.add_edges([{:a, :b, weight: 1}, {:b, :c, weight: 2}])

Graph.edges(g, by: 1)
#=> [%Graph.Edge{v1: :a, v2: :b, weight: 1}]

Partition-filtered traversals

BFS, DFS, Dijkstra, A*, and Bellman-Ford all support a by: option to restrict traversal to edges in specific partitions:

g =
  Graph.new(multigraph: true)
  |> Graph.add_edges([
    {:a, :b, label: :fast, weight: 1},
    {:a, :c, label: :slow, weight: 10},
    {:b, :d, label: :fast, weight: 1},
    {:c, :d, label: :slow, weight: 1}
  ])

# Shortest path using only :fast edges
Graph.dijkstra(g, :a, :d, by: :fast)
#=> [:a, :b, :d]

# BFS following only :fast edges
Graph.Reducers.Bfs.map(g, & &1, by: :fast)
#=> [:a, :b, :d]

Edge properties

Edges now support an arbitrary properties map for storing additional metadata:

g = Graph.new()
|> Graph.add_edge(:a, :b, label: :link, properties: %{color: "red", style: :dashed})

[edge] = Graph.edges(g)
edge.properties
#=> %{color: "red", style: :dashed}

Rationale

The original motivation for me to start working on this library is the fact that :digraph requires a minimum of 3 ETS tables per graph, and up to 6 depending on the operations you are performing on the graph. If you are working with a lot of graphs concurrently, as I am, this means you can find yourself in a situation where you hit the system limit for the maximum number of ETS table, and bring your system down. Seeing as how it is ridiculous that trying to use a simple graph could potentially kill my system, and not wanting to hack around the problem, I decided to see if I could build an alternative which was competitive performance-wise, without requiring any ETS tables at all.

The result turned out better than I hoped - it is possible to build a graph datastructure without ETS that is both equally performant (and in many of my benchmarks, better performing), and supports all of the same functionality.

Additionally, I also had a few other things I wanted to address:

Inconsistency with argument order in the API between :digraph and :digraph_utils
The fact that there are two modules to work with the same datastructure to begin with, and trying to remember what lives where.
The lack of extensibility, for example, there is no API with which you can implement your own traversal algorithms. This means you are stuck with whatever way the Erlang maintainers decided was ideal, regardless of whether it suits your use case or not. A great example is single-source shortest path algorithms, where you may want a simple breadth-first search, or perhaps you want to use Dijkstra's algorithm - you are stuck with just one approach with :digraph, which as I understand it, is a breadth-first search.
:digraph as the name implies, only supports directed graphs
:digraph graphs are unweighted, with no way to supported weighted graphs
:digraph graphs are not "inspect-friendly", you get a tuple with the underlying ETS table ids, but that's it, not necessarily a big deal, but it's nice for playing around in the shell if you can see how your code affects the structure.

My speculation as to why :digraph is the way it is, is that when :digraph was originally written, there was no efficient key/value datastructure in Erlang that could support large numbers of keys. At that time, maps weren't even a speck in the eye of the language maintainers. Even after the initial introduction of maps in OTP 18, maps still weren't efficient enough to work with large numbers of keys. It wasn't until OTP 19 that the performance of maps with millions of keys became reasonable. So, it's not that :digraph sucks - it was the best possible implementation at the time; but now that the language has come so far, we can take advantage of some of the new hotness and reinvent it from the ground up :).

Benchmarks

Feel free to take a look under the bench folder in the project root. There a few benchmarks I threw together to keep an eye on a few key areas I wanted to ensure parity with :digraph on. You can run them yourself as well, but I would encourage you to use them as a template to construct a benchmark based on your own use case, and compare them that way, as it will give you a better basis to make your decision on. However, if you do find that libgraph is behind :digraph with a benchmark, please let me know so that I can improve the library!

NOTE: While this library is primarily focused on the Graph data structure it defines, it also contains an implementation of a priority queue (you can find it under the PriorityQueue module), designed for use with graphs specifically, as it considers lower integer values higher priority, which is perfect for the kinds of graph algorithms you need a priority queue for.

Contributing

To run the test suite you will need to run mix eqc.install --mini once you've cloned the repo and fetched dependencies.

If you have changes in mind that are significant or potentially time consuming, please open a RFC-style PR first, where we can discuss your plans first. I don't want you to spend all your time crafting a PR that I ultimately reject because I don't think it's a good fit or is too large for me to review. Not that I plan to reject PRs in general, but I have to be careful to balance features with maintenance burden, or I will quickly be unable to manage the project.

Please ensure that you adhere to a commit style where logically related changes are in a single commit, or broken up in a way that eases review if necessary. Keep commit subject lines informative, but short, and provide additional detail in the extended message text if needed. If you can, mention relevant issue numbers in either the subject or the extended message.

Roadmap

Please open an issue if you have a feature request!

License

MIT (See the LICENSE file)