Konigsberg Bridge

bridge.js

function generateEdges(graph) {
  var i, node, edges = [];
  
  for (node in graph) {
    graph[node].forEach(function (neighbour) {
      edges.push([node, neighbour]);
    });
  }
  
  return edges;
}

function countEdges(edges) {
  var counts = {};

  edges.forEach(function (edge) {
    if (edge[0] !== edge[1]) {
      edge.forEach(function (e) {
        if (!counts[e])
          counts[e] = 1;
        else
          counts[e]++;
      });
    }
  });

  for (key in counts) {
    counts[key] /= 2;
    if (counts[key] % 2 !== 0)
      odd++;
  }

  counts.possibility = odd === 0 || (odd > 0 && odd === 2);

  return counts;
}

var graph_1 = {
  '1': ['2', '6'],
  '2': ['1', '3', '4', '5'],
  '3': ['2', '7'],
  '4': ['2', '5', '6', '8'],
  '5': ['2', '4', '7', '9'],
  '6': ['1', '4', '8', '10'],
  '7': ['3', '5', '9', '12'],
  '8': ['4', '6', '9', '11'],
  '9': ['5', '7', '8', '11'],
  '10': ['6', '11'],
  '11': ['8', '9', '10', '12'],
  '12': ['7', '11']
};

var graph_2 = {
  '1': ['2', '4', '8'],
  '2': ['1', '3', '4', '5'],
  '3': ['2', '5', '6'],
  '4': ['1', '2', '6', '7'],
  '5': ['2', '3', '7', '8'],
  '6': ['3', '4', '7'],
  '7': ['4', '5', '6', '8'],
  '8': ['1', '5', '7']
};

var edges_1  = generateEdges(graph_1);
var counts_1 = countEdges(edges_1);
//console.log(edges_1);
console.log(counts_1);

var edges_2  = generateEdges(graph_2);
var counts_2 = countEdges(edges_2);
//console.log(edges_2);
console.log(counts_2);