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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 CocoaPodSwiftGraph.

Add the following to yourCartfile:

github "davecom/SwiftGraph" ~> 3.1

Use this repository as your dependency.

Copy all of the sources in theSources folder into your project.

• To get a sense of how to use SwiftGraph, checkout the unit tests
• Inserting an edge by vertex indices is much faster than inserting an edge by vertex objects that need to have their indices looked up
• Generally, looking for the index of a vertex is O(n) time, with n being the number of vertices in the graph
• SwiftGraph includes the functionsbfs() anddfs() for finding a route between one vertex and another in a graph anddijkstra() for finding shortest paths in a weighted graph
• A sample Mac app that implements the Nine Tails problem is included - just change the target of the project toSwiftGraphSampleApp to build it

For more detail, checkout theDocumentation section, but this example building up a weighted graph of American cities and doing some operations on it, should get you started.

letcityGraph:WeightedGraph<String,Int>=WeightedGraph<String,Int>(vertices:["Seattle","San Francisco","Los Angeles","Denver","Kansas City","Chicago","Boston","New York","Atlanta","Miami","Dallas","Houston"])

cityGraph is aWeightedGraph withString vertices andInt weights on its edges.

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 addWeightedEdge connections between various vertices.

let(distances, pathDict)= cityGraph.dijkstra(root:"New York", startDistance:0)varnameDistance:[String:Int?]=distanceArrayToVertexDict(distances: distances, graph: cityGraph)// shortest distance from New York to San Franciscolettemp=nameDistance["San Francisco"] // path between New York and San Franciscoletpath:[WeightedEdge<Int>]=pathDictToPath(from: cityGraph.indexOfVertex("New York")!, to: cityGraph.indexOfVertex("San Francisco")!, pathDict: pathDict)letstops:[String]= cityGraph.edgesToVertices(edges: path)

The shortest paths are found between various vertices in the graph using Dijkstra's algorithm.

letmst= cityGraph.mst()

The minimum spanning tree is found connecting all of the vertices in the graph.

letcycles= cityGraph.detectCycles()

All of the cycles incityGraph are found.

letisADAG= cityGraph.isDAG

isADAG isfalse becausecityGraph is not found to be a Directed Acyclic Graph.

letresult= cityGraph.findAll(from:"New York"){ vinreturn v.characters.first=="S"}

A breadth-first search is performed, starting from New York, for all cities incityGraph that 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 produceHTML 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. AllEdges must beCodable.
• UnweightedEdge - This is a concrete implementation ofEdge for unweighted graphs.
• WeightedEdge - This is a concrete implementation ofEdge for weighted graphs. Weights are a generic type - they can be anything that implementsComparable,Numeric andCodable. Typical weight types areInt andFloat.

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 protocolsCollection (for iterating through all vertices and for grabbing a vertex by its index through a subscript) andCodable . For instance, the following example prints all vertices in a Graph on separate lines:

forvin g{  // g is a Graph<String>print(v)}

And we can grab a specific vertex by its index using a subscript

print(g[23]) // g is a Graph<String>

Note: At this time, graphs arenot 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,UnweightedGraph orWeightedGraph, instead of rolling your own adopter, because they offer significant built-in functionality. The vertices in aGraph (defined as a generic at graph creation time) can be of any type that conforms toEquatable andCodable. AllGraphs areCodable.Graph has methods for:
  • Adding a vertex
  • Getting the index of a vertex
  • Finding the neighbors of an index/vertex
  • Finding the edges of an index/vertex
  • Checking if an edge from one index/vertex to another index/vertex exists
  • Checking if a vertex is in the graph
  • Adding an edge
  • Removing all edges between two indexes/vertices
  • Removing a particular vertex (all other edge relationships are automatically updated at the same time (because the indices of their connections changes) so this is slow - O(v + e) where v is the number of vertices and e is the number of edges)
• UnweightedGraph - A generic class implementation ofGraph that adds convenience methods for adding and removing edges of typeUnweightedEdge.UnweightedGraph is generic over the type of the vertices.
• WeightedGraph - A generic class implementation ofGraph that adds convenience methods for adding and removing edges of typeWeightedEdge.WeightedGraph also adds a method for returning a list of tuples containing all of the neighbor vertices of an index along with their respective weights.WeightedGraph is generic over the types of the vertices and its weights.
• UniqueElementsGraph - aGraph implementation with support for union operations that ensures all vertices and edges in a graph are unique.

Search methods are defined in extensions ofGraph andWeightedGraph inSearch.swift.

• bfs() (method onGraph) - Finds a path from one vertex to another in aGraph using a breadth-first search. Returns an array ofEdges 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 fromgoalTest().
• dfs() (method onGraph) - Finds a path from one vertex to another in aGraph using a depth-first search. Returns an array ofEdges 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 fromgoalTest().
• findAll() Uses a breadth-first search to find all connected vertices from the starting vertex that return true when run through agoalTest() function. Paths to the connected vertices are returned in an array, which is empty if no vertices are found.
• dijkstra() (method onWeightedGraph) - Finds the shortest path from a starting vertex to every other vertex in aWeightedGraph. 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 previousEdge that gets them there in the shortest time from the staring vertex. Using this dictionary and the functionpathDictToPath(), you can find the shortest path from the starting vertex to any other connected vertex. See thedijkstra() unit tests inDijkstraGraphTests.swift for a demo of this.
• Graph traversal versions ofbfs() anddfs() that allow a visit function to execute at each stop

An extension toGraph inSort.swift provides 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 usestopologicalSort() to determine whether a graph is a DAG (directed-acyclic graph). Runs in O(n) time.

An extension toWeightedGraph inMST.swift can 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 ofWeightedEdges that compose the tree. Use utility functionstotalWeight() andprintMST() to examine the returned MST. Runs in O(n lg n) time.

An extension toGraph inCycles.swift finds 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, ifupToLength is 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 toGraph inReversed.swift reverses all of the edges in a graph.

SwiftGraph is written by David Kopec and other contributors (seeCONTRIBUTORS.md). It is released under the Apache License (seeLICENSE). 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). SeeLICENSE for 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 ofGraph
• More extensive performance testing
• GraphML and Other Format Support