An adjacency list and an adjacency matrix are two common ways to represent a graph in computer science.
Adjacency List:
Pros:
Cons:
Adjacency Matrix:
Pros:
Cons:
important note
Graph Traversal
Finding the shortest path BFS would be better
*Directed vs Undirected Graphs: *
A directed graph, also called a digraph, is a graph where each edge has a direction. The edges point from one vertex to another.
An undirected graph is a graph in which edges have no orientation. The edge (x, y) is identical to the edge (y, x).
Weighted vs Unweighted Graphs:
A weighted graph is a graph in which each edge is assigned a weight or cost. This is useful in problems where certain edges have different importance or length.
An unweighted graph is a graph in which all edges are of equal weight or cost.
Self Loop:
Sparse vs Dense Graphs:
A sparse graph is a graph in which the number of edges is close to the minimal number of edges. In other words, there are very few edges between vertices.
A dense graph is a graph in which the number of edges is close to the maximum possible number of edges. In other words, there are many edges between vertices.
Cyclic vs Acyclic Graphs:
A cyclic graph is a graph that contains at least one cycle (a path of edges and vertices wherein a vertex is reachable from itself).
An acyclic graph is a graph with no cycles. A special type of acyclic graph called a tree, is a connected, undirected graph with no cycles.
// Weighted graph adjacency list would look like { 1: [ {node: 2, weight: 50}, {node: 3, weight: 60}] ... 6: [{node: 1, weight: 40}, {node:5, weight:30 }, {node:4, weight: 90}] }
class Graph { constructor() { this.adjList = {}; } addNode(value) { this.adjList[value] = [] } addEdge(node1, node2) { this.adjList[node1].push(node2); this.adjList[node2].push(node1); } removeEdge(node1, node2) { this.removeElement(node1, node2); this.removeElement(node2, node1); } removeElement(node, value) { const index = this.adjList[node].indexOf(value); this.adjList[node] = [...this.adjList[node].slice(0, index), ...this.adjList[node].slice(index+1)]; } removeNode(node) { const connectedNodes = this.adjList[node]; for (let connectedNode of connectedNodes) { this.removeElement(connectedNode, node); } delete this.adjList[node]; } depthFirstTraversal(startNode) { const stack = []; const visited = {}; stack.push(startNode); visited[startNode] = true; while(stack.length > 0) { const currentNode = stack.pop(); const connectedNodes = this.adjList[currentNode]; console.log(currentNode); connectedNodes.forEach(connectedNode => { if (!visited[connectedNode]) { visited[connectedNode] = true; stack.push(connectedNode); } }) } } breathFirstTraversal(startNode) { const queue = []; const visited = {} queue.push(startNode); visited[startNode] = true; while(queue.length > 0) { const currentElement = queue.shift(); const connectedNodes = this.adjList[currentElement]; console.log(currentElement); connectedNodes.forEach(connectedNode => { if (!visited[connectedNode]) { visited[connectedNode]=true; queue.push(connectedNode); } }); } } } const test = new Graph(); test.addNode(1); test.addNode(2); test.addNode(3); test.addNode(4); test.addNode(5); test.addNode(6); test.addEdge(1,2) test.addEdge(1,3) test.addEdge(1,6) test.addEdge(2, 3); test.addEdge(2, 5); test.addEdge(2, 4); test.addEdge(3, 4); test.addEdge(3, 5); test.addEdge(4, 5); test.addEdge(4, 6); test.addEdge(5, 6); console.log('After adding all node and Edge --> ', test.adjList) test.removeNode(4); console.log('After Removing node 4 --> ', test.adjList) console.log('----------Depth First Traversal -------------') test.depthFirstTraversal(1); console.log('----------Breath First Traversal -------------') test.breathFirstTraversal(1); /* After adding all node and Edge --> { '1': [ 2, 3, 6 ], '2': [ 1, 3, 5, 4 ], '3': [ 1, 2, 4, 5 ], '4': [ 2, 3, 5, 6 ], '5': [ 2, 3, 4, 6 ], '6': [ 1, 4, 5 ] } After Removing node 4 --> { '1': [ 2, 3, 6 ], '2': [ 1, 3, 5 ], '3': [ 1, 2, 5 ], '5': [ 2, 3, 6 ], '6': [ 1, 5 ] } ----------Depth First Traversal ------------- 1 6 5 3 2 ----------Breath First Traversal ------------- 1 2 3 6 5 */
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