DSA

Graph Basics

Understand graph representation, terminology, and fundamental graph concepts for solving network problems.

By TechCoder TeamLast updated: 2026-06-02
In a Nutshell

Understand graph representation, terminology, and fundamental graph concepts for solving network problems. This hands-on tutorial focuses on practical implementation of graph basics concepts.

Graph Basics

Graphs model relationships between objects - social networks, maps, dependencies, and more.

Graph Terminology

  • Vertex (Node): An individual record in the graph (A, B, C, D).
  • Edge: The link between two vertices (A-B, A-C, etc.).
  • Directed Graph: Edges have a direction (A $\rightarrow$ B).
  • Undirected Graph: Edges have no direction (A $-$ B).
  • Weighted Graph: Edges have numerical values (distance, cost).

Representation

Adjacency List

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

Space: O(V + E)
Check edge: O(degree)

Adjacency Matrix

# 0=A, 1=B, 2=C, 3=D
graph = [
    [0, 1, 1, 0],
    [1, 0, 0, 1],
    [1, 0, 0, 1],
    [0, 1, 1, 0]
]

Space: O(V²)
Check edge: O(1)

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Quiz

Quiz

Question 1 of 1

What's the space complexity of an adjacency list?

O(V)
O(V + E)
O(V²)
O(E)

Key Takeaways

✅ Graphs model relationships and networks
✅ Adjacency list - space efficient for sparse graphs
✅ Adjacency matrix - fast edge lookup

Essential for social networks, maps, and dependencies! 🚀