Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a vertex in a graph?

A vertex (or node) is a point in a graph where edges meet. It represents an entity or object.

beginner

Define an edge in graph terminology.

An edge is a connection or link between two vertices in a graph. It shows a relationship or path.

beginner

What does it mean if a graph is directed?

A directed graph has edges with a direction, meaning the connection goes from one vertex to another specific vertex.

beginner

Explain an undirected graph.

An undirected graph has edges without direction. The connection between vertices goes both ways equally.

beginner

What is a weighted graph?

A weighted graph has edges that carry a value or weight, like distance or cost, showing how strong or costly the connection is.

In a graph, what is the term for a point where edges meet?

A Vertex

B Edge

C Weight

D Path

A vertex is the point or node where edges connect in a graph.

Which type of graph has edges with directions?

A Directed graph

B Undirected graph

C Weighted graph

D Complete graph

Directed graphs have edges that go from one vertex to another in a specific direction.

What does an edge represent in a graph?

A The weight of a vertex

B A single point

C The color of a node

D A connection between two vertices

An edge connects two vertices, showing a relationship or path.

In an undirected graph, edges are:

A Always weighted

B One-way connections

C Two-way connections

D Not connected

Undirected graphs have edges that connect vertices both ways equally.

What extra information does a weighted graph edge carry?

A Color

B Weight or cost

C Direction

D Shape

Weighted graph edges have values like cost or distance to show strength or expense.

Describe the difference between directed and undirected graphs.

Think about whether edges have arrows or not.

Explain what a weighted graph is and why weights might be useful.

Imagine roads with distances or prices.

Practice

1. In a graph, what do we call the points or nodes where edges meet?

easy

A. Edges

B. Weights

C. Vertices

D. Paths

Solution

1. Step 1: Understand graph components

   A graph consists of points called nodes and connections called edges.

2. Step 2: Identify the term for nodes

   The points or nodes where edges meet are called vertices.

3. Final Answer:

   Vertices -> Option C

4. Quick Check:

   Nodes = Vertices [OK]

Hint: Nodes in graphs are called vertices [OK]

Common Mistakes:

• Confusing edges with vertices
• Thinking weights are nodes
• Mixing paths with nodes

2. Which of the following is the correct way to represent a weighted edge from vertex 1 to vertex 2 with weight 5 in TypeScript?

easy

A. const edge = { 1: 2, 5 };

B. const edge = [1, 2, 5];

C. const edge = (1, 2, 5);

D. const edge = { from: 1, to: 2, weight: 5 };

Solution

1. Step 1: Understand object syntax in TypeScript

   Objects use key-value pairs with curly braces and colons.

2. Step 2: Check each option's syntax

   const edge = { from: 1, to: 2, weight: 5 }; correctly uses keys 'from', 'to', and 'weight' with values. const edge = [1, 2, 5]; is an array, valid but less descriptive. const edge = (1, 2, 5); uses parentheses, invalid for object. const edge = { 1: 2, 5 }; has invalid syntax.

3. Final Answer:

   const edge = { from: 1, to: 2, weight: 5 }; -> Option D

4. Quick Check:

   Object with keys and values = const edge = { from: 1, to: 2, weight: 5 }; [OK]

Hint: Use curly braces and key:value pairs for objects [OK]

Common Mistakes:

• Using parentheses instead of braces
• Incorrect object key syntax
• Confusing arrays with objects

3. What will be the output of the following TypeScript code that creates a directed weighted graph and prints its edges?

type Edge = { from: number; to: number; weight: number };
const graph: Edge[] = [
  { from: 1, to: 2, weight: 3 },
  { from: 2, to: 3, weight: 4 },
  { from: 3, to: 1, weight: 5 }
];
for (const edge of graph) {
  console.log(`${edge.from} -> ${edge.to} (weight: ${edge.weight})`);
}

medium

A. 1 -> 2 (weight: 3)
2 -> 3 (weight: 4)
3 -> 1 (weight: 5)

B. 1 -> 2 (weight: 5)
2 -> 3 (weight: 3)
3 -> 1 (weight: 4)

C. 1 -> 3 (weight: 5)
2 -> 1 (weight: 4)
3 -> 2 (weight: 3)

D. Error: Invalid graph definition

Solution

1. Step 1: Read the graph array

   The graph array has edges: 1->2 with weight 3, 2->3 with weight 4, 3->1 with weight 5.

2. Step 2: Trace the for loop output

   The loop prints each edge in the format 'from -> to (weight: weight)'. So output matches 1 -> 2 (weight: 3) 2 -> 3 (weight: 4) 3 -> 1 (weight: 5) exactly.

3. Final Answer:

   1 -> 2 (weight: 3) 2 -> 3 (weight: 4) 3 -> 1 (weight: 5) -> Option A

4. Quick Check:

   Print edges as defined = 1 -> 2 (weight: 3) 2 -> 3 (weight: 4) 3 -> 1 (weight: 5) [OK]

Hint: Match printed edges exactly as in array order [OK]

Common Mistakes:

• Mixing up weights and vertices
• Reversing edge directions
• Assuming syntax error

4. Identify the error in the following TypeScript code that tries to create an undirected weighted graph:

type Edge = { from: number; to: number; weight: number };
const graph: Edge[] = [
  { from: 1, to: 2, weight: 7 },
  { from: 2, to: 1, weight: 7 },
  { from: 2, to: 3, weight: 5 }
];
function addEdge(from: number, to: number, weight: number) {
  graph.push({ from, to, weight });
  graph.push({ from: to, to: from, weight });
}
addEdge(3, 4, 6);
console.log(graph.length);

medium

A. No error; graph length will be 5

B. Error: Duplicate edges cause conflict

C. Error: addEdge function pushes edges incorrectly

D. Error: graph array is immutable

Solution

1. Step 1: Count initial edges

   Initially, graph has 3 edges: 1->2, 2->1, 2->3.

2. Step 2: Analyze addEdge function call

   addEdge(3, 4, 6) pushes { from: 3, to: 4, weight: 6 } and { from: 4, to: 3, weight: 6 }, adding 2 more edges for undirected graph.

3. Step 3: Calculate final length

   3 initial + 2 added = 5. No errors occur; code runs successfully.

4. Final Answer:

   No error; graph length will be 5 -> Option A

5. Quick Check:

   3 + 2 = 5 [OK]

Hint: Count edges before and after addEdge call [OK]

Common Mistakes:

• Assuming duplicate edges cause error
• Miscounting edges after push
• Thinking graph is immutable

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

const graph: Record = {
  1: [{ node: 2, weight: 4 }, { node: 3, weight: 1 }],
  2: [{ node: 1, weight: 4 }, { node: 3, weight: 2 }, { node: 4, weight: 5 }],
  3: [{ node: 1, weight: 1 }, { node: 2, weight: 2 }, { node: 4, weight: 8 }],
  4: [{ node: 2, weight: 5 }, { node: 3, weight: 8 }]
};

// How to find the total weight of edges connected to vertex 2?

Which code snippet correctly calculates the total weight of edges connected to vertex 2?

hard

A. const total = graph[2].map(edge => edge.weight).length;

B. const total = graph[2].reduce((sum, edge) => sum + edge.weight, 0);

C. const total = graph[2].filter(edge => edge.weight > 0);

D. const total = graph.reduce((sum, edges) => sum + edges.weight, 0);

Solution

1. Step 1: Understand adjacency list structure

   graph[2] is an array of edges connected to vertex 2, each with a weight property.

2. Step 2: Calculate total weight

   Use reduce to sum all edge weights in graph[2]. const total = graph[2].reduce((sum, edge) => sum + edge.weight, 0); correctly sums weights. const total = graph[2].map(edge => edge.weight).length; counts edges, not sum. const total = graph[2].filter(edge => edge.weight > 0); filters edges, no sum. const total = graph.reduce((sum, edges) => sum + edges.weight, 0); tries to reduce graph object, invalid.

3. Final Answer:

   const total = graph[2].reduce((sum, edge) => sum + edge.weight, 0); -> Option B

4. Quick Check:

   Sum weights with reduce = const total = graph[2].reduce((sum, edge) => sum + edge.weight, 0); [OK]

Hint: Use reduce to sum weights in adjacency list [OK]

Common Mistakes:

• Using map length instead of sum
• Filtering without summing
• Reducing wrong data structure