Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Java - Build from Scratch

Understanding Graph Terminology: Vertices, Edges, Directed, Undirected, Weighted

📖 Scenario: Imagine you are organizing a small social network where people are connected as friends. You want to represent these connections using a graph.

🎯 Goal: You will create a simple graph using Java to represent people as vertices and their friendships as edges. You will also mark if the friendships are one-way (directed) or two-way (undirected), and if the connections have a strength (weight).

📋 What You'll Learn

Create a graph with exactly 4 vertices named "Alice", "Bob", "Charlie", and "Diana"

Create edges between these vertices with specified directions and weights

Use a variable to indicate if the graph is directed or undirected

Store weights as integers representing the strength of the connection

Print the graph connections showing vertices, edges, direction, and weights

💡 Why This Matters

🌍 Real World

Graphs are used to model social networks, maps, and many relationships in real life.

💼 Career

Understanding graph basics is essential for software roles involving networking, recommendation systems, and data analysis.

1

Create vertices for the graph

Create a String[] array called vertices with these exact names: "Alice", "Bob", "Charlie", and "Diana".

DSA Java

// Your code here

Hint

Use curly braces {} to list the names inside the array.

2

Set graph type as directed or undirected

Create a boolean variable called isDirected and set it to true to indicate the graph is directed.

DSA Java

String[] vertices = {"Alice", "Bob", "Charlie", "Diana"};
// Your code here

Hint

Use boolean type and assign true or false.

3

Create edges with weights

Create a 2D integer array called weights representing the edges between vertices. Use these exact values:
weights[0][1] = 5 (Alice to Bob),
weights[1][2] = 3 (Bob to Charlie),
weights[2][3] = 4 (Charlie to Diana),
weights[3][0] = 2 (Diana to Alice).
Set all other edges to 0.

DSA Java

String[] vertices = {"Alice", "Bob", "Charlie", "Diana"};
boolean isDirected = true;
// Your code here

Hint

Initialize a 4x4 integer array and assign weights to specific edges.

4

Print graph edges with direction and weights

Use nested for loops to print all edges with weight > 0 in this exact format:
"Alice -> Bob : 5" if isDirected is true, otherwise use "Alice -- Bob : 5".
Print one edge per line.

DSA Java

String[] vertices = {"Alice", "Bob", "Charlie", "Diana"};
boolean isDirected = true;
int[][] weights = new int[4][4];
weights[0][1] = 5;
weights[1][2] = 3;
weights[2][3] = 4;
weights[3][0] = 2;
// Your code here

Hint

Use nested loops to check all pairs and print only edges with weight > 0. Use System.out.println for output.

Practice

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

easy

A. A point or node where edges meet

B. A line connecting two vertices

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 or the whole graph, not vertices.

3. Final Answer:

   A point or node where edges meet -> Option A

4. Quick Check:

   Vertex = point/node [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 declare an undirected weighted graph using adjacency list in Java?

easy

A. Map graph = new HashMap<>();

B. Map graph = new TreeMap<>();

C. Map>> graph = new TreeSet<>();

D. Map>> graph = new HashMap<>();

Solution

1. Step 1: Identify data structure for weighted edges

   Weighted edges need to store both neighbor and weight, so Pair is used.

2. Step 2: Choose correct map and list types

   HashMap with List of pairs is standard for adjacency list of weighted graphs.

3. Final Answer:

   Map>> graph = new HashMap<>(); -> Option D

4. Quick Check:

   Weighted graph uses Pair for edges [OK]

Hint: Weighted edges need pairs: neighbor and weight [OK]

Common Mistakes:

• Using List<Integer> for weighted edges
• Using TreeSet instead of List for adjacency
• Confusing Map types for graph

3. Consider the following Java code snippet for a directed graph:

Map graph = new HashMap<>();
graph.put(1, Arrays.asList(2, 3));
graph.put(2, Arrays.asList(3));
graph.put(3, Arrays.asList());
System.out.println(graph.get(1));

What will be the output?

medium

A. null

B. [1, 2, 3]

C. [2, 3]

D. []

Solution

1. Step 1: Check what is stored for key 1

   Key 1 maps to list containing 2 and 3.

2. Step 2: Print the list for key 1

   Printing graph.get(1) outputs the list [2, 3].

3. Final Answer:

   [2, 3] -> Option C

4. Quick Check:

   graph.get(1) = [2, 3] [OK]

Hint: Print adjacency list for key to see neighbors [OK]

Common Mistakes:

• Expecting all vertices in output
• Confusing keys and values
• Assuming empty list prints null

4. The following code attempts to add an edge to an undirected graph represented by adjacency list. What is the bug?

void addEdge(Map graph, int u, int v) {
    graph.get(u).add(v);
}

medium

A. It adds edge only from u to v, missing v to u

B. It uses get() instead of put() to add edge

C. It should use a Set instead of List for adjacency

D. It should clear the adjacency list before adding

Solution

1. Step 1: Understand undirected graph edge addition

   Undirected edges must be added both ways: u to v and v to u.

2. Step 2: Analyze given code

   Code adds edge only from u to v, missing the reverse edge.

3. Final Answer:

   It adds edge only from u to v, missing v to u -> Option A

4. Quick Check:

   Undirected edges need both directions [OK]

Hint: Undirected edges require adding both directions [OK]

Common Mistakes:

• Adding edge only one way in undirected graph
• Confusing get() and put() usage
• Clearing adjacency list mistakenly

5. You have a weighted directed graph represented as:

Map>> graph = new HashMap<>();
graph.put(1, Arrays.asList(new Pair<>(2, 5), new Pair<>(3, 10)));
graph.put(2, Arrays.asList(new Pair<>(3, 2)));
graph.put(3, Arrays.asList());

How would you find the total weight of edges going out from vertex 1?

hard

A. Sum weights 10 + 2 = 12

B. Sum weights 5 + 10 = 15

C. Sum weights 5 + 2 = 7

D. Count edges: 2

Solution

1. Step 1: Identify edges from vertex 1

   Edges from 1 go to 2 with weight 5, and to 3 with weight 10.

2. Step 2: Sum the weights of these edges

   Total weight = 5 + 10 = 15.

3. Final Answer:

   Sum weights 5 + 10 = 15 -> Option B

4. Quick Check:

   Total outgoing weight from 1 = 15 [OK]

Hint: Add weights of all edges from the vertex [OK]

Common Mistakes:

• Adding weights from wrong vertices
• Counting edges instead of summing weights
• Mixing weights of different edges