eulerian-trail

An implementation of Hierholzer’s Algorithm to find an eulerian trail in a graph

Install

$ npm install --save eulerian-trail

Usage

var eulerianTrail = require('eulerian-trail');
eulerianTrail({
  edges: [
    [0, 1],
    [1, 2],
    [2, 3],
    [3, 6],
    [6, 7],
    [7, 10],
    [0, 10],
    [8, 10],
    [8, 9],
    [9, 10],
    [5, 8],
    [5, 7],
    [7, 8],
    [5, 6],
    [4, 5],
    [3, 4],
    [1, 3],
    [1, 6]
  ]
});
 
// output
// note that the output is reversed from what is shown on the gif
// [ 0, 1, 2, 3, 6, 7, 10, 8, 5, 6, 1, 3, 4, 5, 7, 8, 9, 10, 0 ]

API

eulerianTrail(options)

params

• options.edges {Array[]} (required) An array of arrays, each subarray describes an edge in the graph, the edge must have two primitive elements (numbers and strings are allowed)
• options.directed=false {boolean} True to denote the edges as directed, by default all the edges are undirected

throws

The function throws whenever:

• the graph doesn't fulfill the conditions to be have an eulerian cycle or an eulerian graph, the conditions are
  • if it's undirected it must have 0 or 2 odd degree vertices
  • if it's directed and has the same incoming degree and outgoing degree values and it’s strongly connected or for each vertex for each vertex the difference between its incoming degrees and outgoing degrees is 0 except for 2 vertices whose difference is −1 (start) and +1 (end)
• the trail found doesn't contain all the edges provided in the input

returns {Array}

The eulerian trail from a valid start vertex, each pair of contiguous elements in the output denotes an edge

License

2015 MIT © Mauricio Poppe