ElementaryCycles

Swift port of an algorythm used to find all the cycles in a directed graph:

This is an implementation of an algorithm by Donald B. Johnson to find all elementary cycles in a directed graph (Donald B. Johnson: Finding All the Elementary Circuits of a Directed Graph. SIAM Journal on Computing. Volumne 4, Nr. 1 (1975), pp. 77-84).

Original Java implementation: http://normalisiert.de

Usage

ElementaryCycles

import ElementaryCycles

// dictionary pairs represent node connections from the keys to their values
let graph = ["A": ["B", "C"], "B": ["A"], "C": ["D"], "D": ["C"]]

let cycles = ElementaryCycles.find(graph: graph, sort: { $0 < $1 })

// nodes order is determined by sort parameter 
print(cycles) // [["A", "B"], ["C", "D"]]

• Input: Directed graph

                ┌─────────┐
                ∨         │
    ┌───┐     ┌───┐     ┌───┐
 ┌> │ A │ ──> │ C │ ──> │ D │
 │  └───┘     └───┘     └───┘
 │    │
 │    │
 │    ∨
 │  ┌───┐
 └─ │ B │
    └───┘

• Output: Elementary circuits

 ┌───┐     ┌───┐
 │ A │ ──> │ B │
 └───┘     └───┘
 ┌───┐     ┌───┐
 │ C │ ──> │ D │
 └───┘     └───┘

ElementaryCyclesSearch

Alternatively, you can use ElementaryCyclesSearch library directly, which contains the actual algorythm implementation:

The implementation is pretty much generic, all it needs is a adjacency-matrix of your graph and the objects of your nodes. Then you get back the sets of node-objects which build a cycle.

Original Java implemnetation: http://normalisiert.de

import ElementaryCyclesSearch

let nodes = Vector(["A", "B", "C", "D"])
let matrix = AdjacencyMatrix(4, 4) { matrix in
    matrix[0][1] = true
    matrix[0][2] = true
    matrix[1][0] = true
    matrix[2][3] = true
    matrix[3][2] = true
}
let cycles = getElementaryCycles(adjacencyMatrix: matrix, graphNodes: nodes)

• Input: Node objects

A	B	C	D

• Input: Adjacency-matrix

	A	B	C	D
A	false	true	false	false
B	true	false	false	false
C	true	false	false	true
D	false	false	true	false

• Output: Elementary circuits

 ┌───┐     ┌───┐
 │ A │ ──> │ B │
 └───┘     └───┘
 ┌───┐     ┌───┐
 │ C │ ──> │ D │
 └───┘     └───┘

License

(BSD-2 license)

Original work Copyright (c) 2012, Frank Meyer

All rights reserved.

Swift port Copyright (c) 2018, Hèctor Marquès

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

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