JavaScript Data Structures - Graph

Definition

A graph is a data structure consisting of a set of nodes or vertices and a set of edges that represent connections between those nodes. Graphs can be directed or undirected, while their edges can be assigned numeric weights.

Each node in a graph data structure must have the following properties:

• key: The key of the node
• value: The value of the node

Each edge in a grpah data structure must have the following properties:

• a: The starting node of the edge
• b: The target node of the edge
• weight: An optional numeric weight value for the edge

The main operations of a graph data structure are:

• addNode: Inserts a new node with the specific key and value
• addEdge: Inserts a new edge between two given nodes, optionally setting its weight
• removeNode: Removes the node with the specified key
• removeEdge: Removes the edge between two given nodes
• findNode: Retrieves the node with the given key
• hasEdge: Checks if the graph has an edge between two given nodes
• setEdgeWeight: Sets the weight of a given edge
• getEdgeWeight: Gets the weight of a given edge
• adjacent: Finds all nodes for which an edge exists from a given node
• indegree: Calculates the total number of edges to a given node
• outdegree: Calculates the total number of edges from a given node

Implementation

class Graph {
  constructor(directed = true) {
    this.directed = directed;
    this.nodes = [];
    this.edges = new Map();
  }

  addNode(key, value = key) {
    this.nodes.push({ key, value });
  }

  addEdge(a, b, weight) {
    this.edges.set(JSON.stringify([a, b]), { a, b, weight });
    if (!this.directed)
      this.edges.set(JSON.stringify([b, a]), { a: b, b: a, weight });
  }

  removeNode(key) {
    this.nodes = this.nodes.filter(n => n.key !== key);
    [...this.edges.values()].forEach(({ a, b }) => {
      if (a === key || b === key) this.edges.delete(JSON.stringify([a, b]));
    });
  }

  removeEdge(a, b) {
    this.edges.delete(JSON.stringify([a, b]));
    if (!this.directed) this.edges.delete(JSON.stringify([b, a]));
  }

  findNode(key) {
    return this.nodes.find(x => x.key === key);
  }

  hasEdge(a, b) {
    return this.edges.has(JSON.stringify([a, b]));
  }

  setEdgeWeight(a, b, weight) {
    this.edges.set(JSON.stringify([a, b]), { a, b, weight });
    if (!this.directed)
      this.edges.set(JSON.stringify([b, a]), { a: b, b: a, weight });
  }

  getEdgeWeight(a, b) {
    return this.edges.get(JSON.stringify([a, b])).weight;
  }

  adjacent(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (a === key) acc.push(b);
      return acc;
    }, []);
  }

  indegree(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (b === key) acc++;
      return acc;
    }, 0);
  }

  outdegree(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (a === key) acc++;
      return acc;
    }, 0);
  }
}

• Create a class with a constructor that initializes an empty array, nodes, and a Map, edges, for each instance. The optional argument, directed, specifies if the graph is directed or not.

• Define an addNode() method, which uses Array.prototype.push() to add a new node in the nodes array.

• Define an addEdge() method, which uses Map.prototype.set() to add a new edge to the edges Map, using JSON.stringify() to produce a unique key.

• Define a removeNode() method, which uses Array.prototype.filter() and Map.prototype.delete() to remove the given node and any edges connected to it.

• Define a removeEdge() method, which uses Map.prototype.delete() to remove the given edge.

• Define a findNode() method, which uses Array.prototype.find() to return the given node, if any.

• Define a hasEdge() method, which uses Map.prototype.has() and JSON.stringify() to check if the given edge exists in the edges Map.

• Define a setEdgeWeight() method, which uses Map.prototype.set() to set the weight of the appropriate edge, whose key is produced by JSON.stringify().

• Define a getEdgeWeight() method, which uses Map.prototype.get() to get the eight of the appropriate edge, whose key is produced by JSON.stringify().

• Define an adjacent() method, which uses Map.prototype.values(), Array.prototype.reduce() and Array.prototype.push() to find all nodes connected to the given node.

• Define an indegree() method, which uses Map.prototype.values() and Array.prototype.reduce() to count the number of edges to the given node.

• Define an outdegree() method, which uses Map.prototype.values() and Array.prototype.reduce() to count the number of edges from the given node.

const g = new Graph();

g.addNode('a');
g.addNode('b');
g.addNode('c');
g.addNode('d');

g.addEdge('a', 'c');
g.addEdge('b', 'c');
g.addEdge('c', 'b');
g.addEdge('d', 'a');

g.nodes.map(x => x.value);  // ['a', 'b', 'c', 'd']
[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['a => c', 'b => c', 'c => b', 'd => a']

g.adjacent('c');            // ['b']

g.indegree('c');            // 2
g.outdegree('c');           // 1

g.hasEdge('d', 'a');        // true
g.hasEdge('a', 'd');        // false

g.removeEdge('c', 'b');

[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['a => c', 'b => c', 'd => a']

g.removeNode('c');

g.nodes.map(x => x.value);  // ['a', 'b', 'd']
[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['d => a']

g.setEdgeWeight('d', 'a', 5);
g.getEdgeWeight('d', 'a');  // 5