A Graph Data Structure in Pure Swift
SwiftGraph is a pure Swift (no Cocoa) implementation of a graph data structure, appropriate for use on all platforms Swift supports (iOS, macOS, Linux, etc.). It includes support for weighted, unweighted, directed, and undirected graphs. It uses generics to abstract away both the type of the vertices, and the type of the weights.
It includes copious in-source documentation, unit tests, as well as search functions for doing things like breadth-first search, depth-first search, and Dijkstra's algorithm. Further, it includes utility functions for topological sort, Jarnik's algorithm to find a minimum-spanning tree, detecting a DAG (directed-acyclic-graph), enumerating all cycles, and more.
SwiftGraph 3.0 and above requires Swift 5 (Xcode 10.2). Use SwiftGraph 2.0 for Swift 4.2 (Xcode 10.1) support, SwiftGraph 1.5.1 for Swift 4.1 (Xcode 9), SwiftGraph 1.4.1 for Swift 3 (Xcode 8), SwiftGraph 1.0.6 for Swift 2 (Xcode 7), and SwiftGraph 1.0.0 for Swift 1.2 (Xcode 6.3) support. SwiftGraph supports GNU/Linux and is tested on it.
Use the CocoaPod
SwiftGraph.
Add the following to your
Cartfile:
github "davecom/SwiftGraph" ~> 3.1
Use this repository as your dependency.
Copy all of the sources in the
Sourcesfolder into your project.
bfs()and
dfs()for finding a route between one vertex and another in a graph and
dijkstra()for finding shortest paths in a weighted graph
SwiftGraphSampleAppto build it
For more detail, checkout the Documentation section, but this example building up a weighted graph of American cities and doing some operations on it, should get you started.
let cityGraph: WeightedGraph = WeightedGraph(vertices: ["Seattle", "San Francisco", "Los Angeles", "Denver", "Kansas City", "Chicago", "Boston", "New York", "Atlanta", "Miami", "Dallas", "Houston"])
cityGraphis a
WeightedGraphwith
Stringvertices and
Intweights on its edges.
swift cityGraph.addEdge(from: "Seattle", to:"Chicago", weight:2097) cityGraph.addEdge(from: "Seattle", to:"Chicago", weight:2097) cityGraph.addEdge(from: "Seattle", to: "Denver", weight:1331) cityGraph.addEdge(from: "Seattle", to: "San Francisco", weight:807) cityGraph.addEdge(from: "San Francisco", to: "Denver", weight:1267) cityGraph.addEdge(from: "San Francisco", to: "Los Angeles", weight:381) cityGraph.addEdge(from: "Los Angeles", to: "Denver", weight:1015) cityGraph.addEdge(from: "Los Angeles", to: "Kansas City", weight:1663) cityGraph.addEdge(from: "Los Angeles", to: "Dallas", weight:1435) cityGraph.addEdge(from: "Denver", to: "Chicago", weight:1003) cityGraph.addEdge(from: "Denver", to: "Kansas City", weight:599) cityGraph.addEdge(from: "Kansas City", to: "Chicago", weight:533) cityGraph.addEdge(from: "Kansas City", to: "New York", weight:1260) cityGraph.addEdge(from: "Kansas City", to: "Atlanta", weight:864) cityGraph.addEdge(from: "Kansas City", to: "Dallas", weight:496) cityGraph.addEdge(from: "Chicago", to: "Boston", weight:983) cityGraph.addEdge(from: "Chicago", to: "New York", weight:787) cityGraph.addEdge(from: "Boston", to: "New York", weight:214) cityGraph.addEdge(from: "Atlanta", to: "New York", weight:888) cityGraph.addEdge(from: "Atlanta", to: "Dallas", weight:781) cityGraph.addEdge(from: "Atlanta", to: "Houston", weight:810) cityGraph.addEdge(from: "Atlanta", to: "Miami", weight:661) cityGraph.addEdge(from: "Houston", to: "Miami", weight:1187) cityGraph.addEdge(from: "Houston", to: "Dallas", weight:239)Convenience methods are used to add
WeightedEdgeconnections between various vertices.
swift let (distances, pathDict) = cityGraph.dijkstra(root: "New York", startDistance: 0) var nameDistance: [String: Int?] = distanceArrayToVertexDict(distances: distances, graph: cityGraph) // shortest distance from New York to San Francisco let temp = nameDistance["San Francisco"] // path between New York and San Francisco let path: [WeightedEdge] = pathDictToPath(from: cityGraph.indexOfVertex("New York")!, to: cityGraph.indexOfVertex("San Francisco")!, pathDict: pathDict) let stops: [String] = cityGraph.edgesToVertices(edges: path)The shortest paths are found between various vertices in the graph using Dijkstra's algorithm.
swift let mst = cityGraph.mst()The minimum spanning tree is found connecting all of the vertices in the graph.
swift let cycles = cityGraph.detectCycles()All of the cycles in
cityGraphare found.
swift let isADAG = cityGraph.isDAG
isADAGis
falsebecause
cityGraphis not found to be a Directed Acyclic Graph.
swift let result = cityGraph.findAll(from: "New York") { v in return v.characters.first == "S" }A breadth-first search is performed, starting from New York, for all cities in
cityGraphthat start with the letter "S."
SwiftGraph contains many more useful features, but hopefully this example was a nice quickstart.
There is a large amount of documentation in the source code using the latest Apple documentation technique—so you should be able to just alt-click a method name to get a lot of great information about it in Xcode. We also use Jazzy to produce HTML Docs. In addition, here's an overview of each of SwiftGraph's components:
Edges connect the vertices in your graph to one another.
Edge(Protocol) - A protocol that all edges in a graph must conform to. An edge is a connection between two vertices in the graph. The vertices are specified by their index in the graph which is an integer. All
Edges must be
Codable.
UnweightedEdge- This is a concrete implementation of
Edgefor unweighted graphs.
WeightedEdge- This is a concrete implementation of
Edgefor weighted graphs. Weights are a generic type - they can be anything that implements
Comparable,
Numericand
Codable. Typical weight types are
Intand
Float.
Graphs are the data structures at the heart of SwiftGraph. All vertices are assigned an integer index when they are inserted into a graph and it's generally faster to refer to them by their index than by the vertex's actual object.
Graphs implement the standard Swift protocols
Collection(for iterating through all vertices and for grabbing a vertex by its index through a subscript) and
Codable. For instance, the following example prints all vertices in a Graph on separate lines:
swift for v in g { // g is a Graph print(v) }And we can grab a specific vertex by its index using a subscript
swift print(g[23]) // g is a Graph
Note: At this time, graphs are not thread-safe. However, once a graph is constructed, if you will only be doing lookups and searches through it (no removals of vertices/edges and no additions of vertices/edges) then you should be able to do that from multiple threads. A fully thread-safe graph implementation is a possible future direction.
Graph(Protocol) - This is the base protocol for all graphs. Generally, you should use one of its canonical class implementations,
UnweightedGraphor
WeightedGraph, instead of rolling your own adopter, because they offer significant built-in functionality. The vertices in a
Graph(defined as a generic at graph creation time) can be of any type that conforms to
Equatableand
Codable. All
Graphs are
Codable.
Graphhas methods for:
UnweightedGraph- A generic class implementation of
Graphthat adds convenience methods for adding and removing edges of type
UnweightedEdge.
UnweightedGraphis generic over the type of the vertices.
WeightedGraph- A generic class implementation of
Graphthat adds convenience methods for adding and removing edges of type
WeightedEdge.
WeightedGraphalso adds a method for returning a list of tuples containing all of the neighbor vertices of an index along with their respective weights.
WeightedGraphis generic over the types of the vertices and its weights.
UniqueElementsGraph- a
Graphimplementation with support for union operations that ensures all vertices and edges in a graph are unique.
Search methods are defined in extensions of
Graphand
WeightedGraphin
Search.swift. *
bfs()(method on
Graph) - Finds a path from one vertex to another in a
Graphusing a breadth-first search. Returns an array of
Edges going from the source vertex to the destination vertex or an empty array if no path could be found. A version of this method takes a function,
goalTest(), that operates on a vertex and returns a boolean to indicate whether it is a goal for the search. It returns a path to the first vertex that returns true from
goalTest(). *
dfs()(method on
Graph) - Finds a path from one vertex to another in a
Graphusing a depth-first search. Returns an array of
Edges going from the source vertex to the destination vertex or an empty array if no path could be found. A version of this method takes a function,
goalTest(), that operates on a vertex and returns a boolean to indicate whether it is a goal for the search. It returns a path to the first vertex that returns true from
goalTest(). *
findAll()Uses a breadth-first search to find all connected vertices from the starting vertex that return true when run through a
goalTest()function. Paths to the connected vertices are returned in an array, which is empty if no vertices are found. *
dijkstra()(method on
WeightedGraph) - Finds the shortest path from a starting vertex to every other vertex in a
WeightedGraph. Returns a tuple who's first element is an array of the distances to each vertex in the graph arranged by index. The second element of the tuple is a dictionary mapping graph indices to the previous
Edgethat gets them there in the shortest time from the staring vertex. Using this dictionary and the function
pathDictToPath(), you can find the shortest path from the starting vertex to any other connected vertex. See the
dijkstra()unit tests in
DijkstraGraphTests.swiftfor a demo of this. * Graph traversal versions of
bfs()and
dfs()that allow a visit function to execute at each stop
An extension to
Graphin
Sort.swiftprovides facilities for topological sort and detecting a DAG. *
topologicalSort()- Does a topological sort of the vertices in a given graph if possible (returns nil if it finds a cycle). Returns a sorted list of the vertices. Runs in O(n) time. *
isDAG- A property that uses
topologicalSort()to determine whether a graph is a DAG (directed-acyclic graph). Runs in O(n) time.
An extension to
WeightedGraphin
MST.swiftcan find a minimum-spanning tree from a weighted graph. *
mst()- Uses Jarnik's Algorithm (aka Prim's Algorithm) to find the tree made of minimum cumulative weight that connects all vertices in a weighted graph. This assumes the graph is completely undirected and connected. If the graph has directed edges, it may not return the right answer. Also, if the graph is not fully connected it will create the tree for the connected component that the starting vertex is a part of. Returns an array of
WeightedEdges that compose the tree. Use utility functions
totalWeight()and
printMST()to examine the returned MST. Runs in O(n lg n) time.
An extension to
Graphin
Cycles.swiftfinds all of the cycles in a graph. *
detectCycles()- Uses an algorithm developed by Liu/Wang to find all of the cycles in a graph. Optionally, this method can take one parameter,
upToLength, that specifies a length at which to stop searching for cycles. For instance, if
upToLengthis 3,
detectCycles()will find all of the 1 vertex cycles (self-cycles, vertices with edges to themselves), and 3 vertex cycles (connection to another vertex and back again, present in all undirected graphs with more than 1 vertex). There is no such thing as a 2 vertex cycle.
An extension to
Graphin
Reversed.swiftreverses all of the edges in a graph.
SwiftGraph is written by David Kopec and other contributors (see
CONTRIBUTORS.md). It is released under the Apache License (see
LICENSE). You can find my email address on my GitHub profile page. I encourage you to submit pull requests and open issues here on GitHub.
I would like to thank all of the contributors who have helped improve SwiftGraph over the years, and have kept me motivated. Contributing to SwiftGraph, in-line with the Apache license, means also releasing your contribution under the same license as the original project. However, the Apache license is permissive, and you are free to include SwiftGraph in a commercial, closed source product as long as you give it & its author credit (in fact SwiftGraph has already found its way into several products). See
LICENSEfor details.
If you use SwiftGraph in your product, please let me know by getting in touch with me. It's just cool to know.
Future directions for this project to take could include: * More utility functions * A thread safe implementation of
Graph* More extensive performance testing * GraphML and Other Format Support