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

Recall & Review

beginner

What is a vertex in a graph?

A vertex (or node) is a fundamental part of a graph representing a point or position where edges meet. Think of it like a city on a map.

beginner

What is an edge in a graph?

An edge connects two vertices in a graph. It represents a relationship or path between points, like a road connecting two cities.

beginner

What does it mean if a graph is directed?

A directed graph has edges with a direction, like one-way streets. Each edge goes from one vertex to another in a specific direction.

beginner

What is an undirected graph?

An undirected graph has edges without direction. The connection between vertices works both ways, like a two-way street.

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What is a weighted edge in a graph?

A weighted edge has a number (weight) showing cost, distance, or value of the connection. For example, the length of a road or price of a flight.

In a graph, what does a vertex represent?

A A point or node

B A connection between points

C A direction of travel

D A weight or cost

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

What type of graph has edges with directions?

A Weighted graph

B Directed graph

C Undirected graph

D Complete graph

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

Which graph type allows travel both ways between connected vertices?

A Disconnected graph

B Directed graph

C Weighted graph

D Undirected graph

Undirected graphs have edges without direction, allowing two-way travel.

What does a weighted edge in a graph represent?

A A direction

B A disconnected node

C A cost or value

D A vertex

Weighted edges carry a number showing cost, distance, or value of the connection.

Which of these is NOT a part of graph terminology?

A Array

B Vertex

C Node

D Edge

Array is a data structure, not a graph term.

Explain the difference between directed and undirected graphs with examples.

Think about how roads can allow traffic in one or both directions.

Describe what weighted edges are and why they are useful in graphs.

Consider how a map might show distances or toll costs on roads.

Practice

1. Which of the following best describes a vertex in a graph?

easy

A. A point or node representing an entity in the graph

B. A connection between two nodes

C. A path that starts and ends at the same node

D. A graph with no edges

Solution

1. Step 1: Understand the definition of vertex

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

2. Step 2: Differentiate vertex from edges and other terms

   Edges connect vertices; paths and graph types are different concepts.

3. Final Answer:

   A point or node representing an entity in the graph -> Option A

4. Quick Check:

   Vertex = node/entity [OK]

Hint: Vertices are the points or nodes in a graph [OK]

Common Mistakes:

• Confusing vertices with edges
• Thinking vertices are paths
• Mixing vertex with graph types

2. Which of the following is the correct way to represent a weighted edge from vertex u to vertex v with weight 5 in C struct?

easy

A. struct Edge { int u, v; }; struct Weight { int w; };

B. struct Edge { int u; int v; }; int weight = 5;

C. struct Edge { int u; int v; int weight; };

D. struct Edge { int u; int v; };

Solution

1. Step 1: Identify the correct struct fields for weighted edge

   A weighted edge needs source vertex, destination vertex, and weight as fields.

2. Step 2: Check struct syntax correctness

   struct Edge { int u; int v; int weight; }; correctly declares all three fields in one struct.

3. Final Answer:

   struct Edge { int u; int v; int weight; }; -> Option C

4. Quick Check:

   Weighted edge struct = u, v, weight [OK]

Hint: Weighted edges need u, v, and weight fields in one struct [OK]

Common Mistakes:

• Separating weight outside the edge struct
• Incorrect field order causing confusion
• Missing weight field

3. What is the output of the following code snippet that prints edges of a directed weighted graph?

typedef struct { int u; int v; int weight; } Edge;
Edge edges[] = { {0, 1, 10}, {1, 2, 20}, {2, 0, 30} };
int n = 3;
for (int i = 0; i < n; i++) {
    printf("%d -> %d (weight %d)\n", edges[i].u, edges[i].v, edges[i].weight);
}

medium

A. 0 -> 1 (weight 10)
1 -> 2 (weight 30)
2 -> 0 (weight 20)

B. 0 -> 1 (weight 10)
1 -> 2 (weight 20)
2 -> 0 (weight 30)

C. 0 -> 1 (weight 30)
1 -> 2 (weight 20)
2 -> 0 (weight 10)

D. 1 -> 0 (weight 10)
2 -> 1 (weight 20)
0 -> 2 (weight 30)

Solution

1. Step 1: Read the edges array values

   Edges are: (0,1,10), (1,2,20), (2,0,30).

2. Step 2: Trace the loop printing each edge

   Loop prints each edge in order with format "u -> v (weight w)".

3. Final Answer:

   0 -> 1 (weight 10) 1 -> 2 (weight 20) 2 -> 0 (weight 30) -> Option B

4. Quick Check:

   Print edges as stored = 0 -> 1 (weight 10) 1 -> 2 (weight 20) 2 -> 0 (weight 30) [OK]

Hint: Print edges in array order with their weights [OK]

Common Mistakes:

• Reversing u and v in print
• Mixing up weights between edges
• Printing edges in wrong order

4. Identify the error in this code snippet that tries to create an undirected graph edge list:

typedef struct { int u; int v; } Edge;
Edge edges[2];
edges[0].u = 0; edges[0].v = 1;
edges[1].u = 1; edges[1].v = 0;
// Print edges
for (int i = 0; i <= 2; i++) {
    printf("Edge from %d to %d\n", edges[i].u, edges[i].v);
}

medium

A. Edge direction is incorrect for undirected graph

B. Edges should have weight field

C. Edges array size should be 1, not 2

D. Loop condition should be i < 2, not i <= 2

Solution

1. Step 1: Check array size and loop bounds

   Edges array has size 2, valid indices are 0 and 1.

2. Step 2: Identify loop error

   Loop runs from i=0 to i=2 inclusive, which accesses edges[2] (out of bounds).

3. Final Answer:

   Loop condition should be i < 2, not i <= 2 -> Option D

4. Quick Check:

   Array size 2 means max index 1 [OK]

Hint: Loop index must be less than array size [OK]

Common Mistakes:

• Using <= instead of < in loop
• Assuming edges need weight for undirected
• Confusing edge direction in undirected graphs

5. You have a weighted undirected graph with vertices 0, 1, 2 and edges:
(0,1,4), (1,2,6), (0,2,5)
How many edges will be stored if you represent this graph using an edge list storing each edge only once?

medium

A. 3

B. 6

C. 2

D. 1

Solution

1. Step 1: Understand undirected edge storage

   In undirected graphs, each edge connects two vertices without direction, so store only one entry per edge.

2. Step 2: Count unique edges given

   Edges are (0,1), (1,2), (0,2) -- total 3 unique edges.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Undirected edges stored once = 3 [OK]

Hint: Undirected edges stored once, count unique pairs [OK]

Common Mistakes:

• Counting each edge twice
• Confusing directed with undirected storage
• Ignoring weights when counting edges