Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of adjacency list for an undirected graph

What is the printed adjacency list after adding edges to an undirected graph with vertices 1, 2, 3?

DSA Javascript

class Graph {
  constructor() {
    this.adjList = {};
  }
  addVertex(v) {
    if (!this.adjList[v]) this.adjList[v] = [];
  }
  addEdge(v, w) {
    this.adjList[v].push(w);
    this.adjList[w].push(v);
  }
}

const g = new Graph();
g.addVertex(1);
g.addVertex(2);
g.addVertex(3);
g.addEdge(1, 2);
g.addEdge(2, 3);
console.log(g.adjList);

A {"1":[2],"2":[1,3],"3":[2]}

B {"1":[2],"2":[3],"3":[2]}

C {"1":[2],"2":[1],"3":[2]}

D {"1":[2,3],"2":[1,3],"3":[2,1]}

💡 Hint

Remember that in an undirected graph, edges are added both ways between vertices.

The addEdge method adds each vertex to the other's adjacency list, so vertex 1 connects to 2, vertex 2 connects to 1 and 3, and vertex 3 connects to 2.

❓ Predict Output

intermediate

Output of adjacency list for a directed weighted graph

What is the printed adjacency list after adding weighted edges to a directed graph with vertices 'A', 'B', 'C'?

DSA Javascript

class Graph {
  constructor() {
    this.adjList = {};
  }
  addVertex(v) {
    if (!this.adjList[v]) this.adjList[v] = [];
  }
  addEdge(v, w, weight) {
    this.adjList[v].push({node: w, weight});
  }
}

const g = new Graph();
g.addVertex('A');
g.addVertex('B');
g.addVertex('C');
g.addEdge('A', 'B', 5);
g.addEdge('B', 'C', 3);
console.log(g.adjList);

A {"A":["B"],"B":[{"node":"C","weight":3}],"C":[]}

B {"A":[{"node":"B","weight":3}],"B":[{"node":"C","weight":5}],"C":[]}

C {"A":[{"node":"B","weight":5}],"B":["C"],"C":[]}

D {"A":[{"node":"B","weight":5}],"B":[{"node":"C","weight":3}],"C":[]}

💡 Hint

In a directed weighted graph, edges have direction and weights stored as objects.

Edges are stored only from source to destination with weight. 'A' connects to 'B' with weight 5, 'B' connects to 'C' with weight 3, 'C' has no outgoing edges.

🧠 Conceptual

advanced

Identify the graph type from description

Which graph type is described as having edges with no direction and weights assigned to each edge?

A Undirected weighted graph

B Directed weighted graph

C Directed unweighted graph

D Undirected unweighted graph

💡 Hint

Edges without direction mean connections go both ways.

An undirected weighted graph has edges that connect vertices both ways and each edge has a weight.

❓ Predict Output

advanced

Output of adjacency matrix for directed graph

What is the adjacency matrix after adding edges (0->1), (1->2), (2->0) to a directed graph with 3 vertices?

DSA Javascript

const vertices = 3;
const matrix = Array(vertices).fill(null).map(() => Array(vertices).fill(0));

function addEdge(m, from, to) {
  m[from][to] = 1;
}

addEdge(matrix, 0, 1);
addEdge(matrix, 1, 2);
addEdge(matrix, 2, 0);
console.log(matrix);

A [[0,1,1],[0,0,1],[1,0,0]]

B [[0,1,0],[0,0,1],[1,0,0]]

C [[0,0,1],[0,0,1],[1,0,0]]

D [[0,1,0],[1,0,1],[0,0,0]]

💡 Hint

In adjacency matrix for directed graph, only the [from][to] cell is set to 1.

Edges 0->1, 1->2, 2->0 set matrix[0][1], matrix[1][2], matrix[2][0] to 1. Others remain 0.

🧠 Conceptual

expert

Number of edges in a complete undirected graph

How many edges are there in a complete undirected graph with 7 vertices?

A 14

B 42

C 21

D 49

💡 Hint

Use the formula n*(n-1)/2 for edges in a complete undirected graph.

A complete undirected graph with n vertices has n*(n-1)/2 edges. For n=7, edges = 7*6/2 = 21.

Practice

1. In graph terminology, what is a vertex?

easy

A. A line connecting two nodes

B. A point or node in the graph where edges meet

C. A graph with no edges

D. A graph that has weights on edges

Solution

1. Step 1: Understand the definition of vertex

   A vertex is a fundamental unit in a graph representing a point or node.

2. Step 2: Differentiate vertex from edges and graph types

   Edges connect vertices; weights and graph types describe edges, not vertices.

3. Final Answer:

   A point or node in the graph where edges meet -> Option B

4. Quick Check:

   Vertex = node/point [OK]

Hint: Vertices are points/nodes, edges are connections [OK]

Common Mistakes:

• Confusing edges with vertices
• Thinking weights define vertices
• Mixing graph types with vertex definition

2. Which of the following is the correct way to represent a directed edge from vertex A to vertex B in JavaScript adjacency list?

easy

A. { A: ['B'], B: ['A'] }

B. { A: [], B: ['A'] }

C. { A: ['B'], B: [] }

D. { A: [], B: [] }

Solution

1. Step 1: Understand adjacency list for directed edges

   In a directed graph, an edge from A to B means B is in A's adjacency list.

2. Step 2: Check each option's adjacency list

   { A: ['B'], B: [] } shows B in A's list and empty list for B, correctly representing A -> B.

3. Final Answer:

   { A: ['B'], B: [] } -> Option C

4. Quick Check:

   Directed edge A->B means B in A's list [OK]

Hint: Directed edge means target vertex in source's adjacency list [OK]

Common Mistakes:

• Adding reverse edge for directed graph
• Leaving adjacency list empty for source vertex
• Confusing undirected with directed representation

3. What will be the output of the following JavaScript code representing an undirected weighted graph adjacency list?

const graph = {
  A: [{ node: 'B', weight: 3 }, { node: 'C', weight: 5 }],
  B: [{ node: 'A', weight: 3 }],
  C: [{ node: 'A', weight: 5 }]
};

console.log(graph['A'][1].weight);

medium

A. 5

B. Error

C. undefined

D. 3

Solution

1. Step 1: Access the adjacency list for vertex 'A'

   graph['A'] is an array with two objects: first with weight 3, second with weight 5.

2. Step 2: Access the second element's weight

   graph['A'][1] is the second object { node: 'C', weight: 5 }, so weight is 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   graph['A'][1].weight = 5 [OK]

Hint: Index 1 means second element; check its weight property [OK]

Common Mistakes:

• Confusing index 0 and 1
• Accessing weight on wrong node
• Assuming undirected means no weights

4. Identify the error in this JavaScript code snippet representing a directed graph adjacency list:

const graph = {
  A: ['B'],
  B: ['C'],
  C: ['A']
};

// Add edge from B to A
graph.B.push('A');

// Add edge from C to B
graph.C.push('B');

console.log(graph);

medium

A. Edges added duplicate existing edges incorrectly

B. Edges added create a cycle, which is invalid

C. The graph object is mutated incorrectly causing unexpected behavior

D. No error, code correctly adds edges

Solution

1. Step 1: Check initial graph structure

   Graph has directed edges A->B, B->C, C->A forming a cycle, which is allowed.

2. Step 2: Verify edge additions

   Adding B->A and C->B edges extends the graph; push method correctly mutates adjacency lists.

3. Final Answer:

   No error, code correctly adds edges -> Option D

4. Quick Check:

   push adds edges correctly; cycles allowed [OK]

Hint: push adds edges; cycles allowed in directed graphs [OK]

Common Mistakes:

• Thinking cycles are invalid in directed graphs
• Assuming push does not mutate arrays
• Confusing undirected with directed edge additions

5. You have an undirected weighted graph represented as an adjacency list in JavaScript:

const graph = {
  A: [{ node: 'B', weight: 2 }, { node: 'C', weight: 4 }],
  B: [{ node: 'A', weight: 2 }, { node: 'C', weight: 1 }],
  C: [{ node: 'A', weight: 4 }, { node: 'B', weight: 1 }]
};

Which of the following statements is true about the edge weights?

hard

A. Weights are symmetric; weight from A to B equals weight from B to A

B. Weights differ for edges in opposite directions

C. Weights are ignored in undirected graphs

D. Weights must be zero for undirected edges

Solution

1. Step 1: Understand undirected weighted graph property

   In undirected graphs, edges have no direction, so weights between two vertices are equal both ways.

2. Step 2: Check given adjacency lists for symmetry

   Weight from A to B is 2, and from B to A is also 2; similarly for other edges.

3. Final Answer:

   Weights are symmetric; weight from A to B equals weight from B to A -> Option A

4. Quick Check:

   Undirected edge weights are symmetric [OK]

Hint: Undirected edges have equal weights both ways [OK]

Common Mistakes:

• Assuming weights differ by direction in undirected graphs
• Ignoring weights in undirected graphs
• Thinking weights must be zero