📊 Graph Theory Implementations in Java

Welcome to the Graph Theory Implementations in Java repository! This project contains a collection of Graph Theory algorithms implemented in Java, which include fundamental algorithms for Graph Traversal, Shortest Path, Minimum Spanning Tree, and more.

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🚀 Features

• Graph Traversal Algorithms:
  • Breadth-First Search (BFS) 🧠
  • Depth-First Search (DFS) 🔍
• Shortest Path Algorithms:
  • Dijkstra’s Algorithm 🌐
• Minimum Spanning Tree Algorithms:
  • Kruskal’s Algorithm 🛠️
  • Prim’s Algorithm 🌳
• Cycle Detection & Graph Connectivity:
  • Detect cycles in both directed and undirected graphs 🔄
  • Identify connected components of a graph 🌐

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🛠️ Technologies Used

• Java: The programming language used to implement all the graph theory algorithms.
• Graph Data Structures: Custom data structure to represent graphs, including vertices and edges.
• Priority Queue: Utilized in Dijkstra and Prim’s algorithms for efficient edge selections.

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📌 Getting Started

Follow these steps to get the project running locally:

Step 1: Clone the Repository

git clone https://github.com/bish9oi/Graph-Theory-Implementations-in-Java.git
cd Graph-Theory-Implementations-in-Java

📊 Algorithms Explained

1️⃣ Breadth-First Search (BFS) 🧠

-Time Complexity: O(V + E)

-Space Complexity: O(V)

Concept: Explores the graph level by level starting from the source node.

2️⃣ Depth-First Search (DFS) 🔍

-Time Complexity: O(V + E)

-Space Complexity: O(V)

Concept: Explores the graph by going as deep as possible before backtracking.

3️⃣ Dijkstra’s Algorithm 🌐

-Time Complexity: O(E + V log V)

-Space Complexity: O(V)

Concept: Finds the shortest path from a source node to all other nodes in a weighted graph.

5️⃣ Kruskal’s Algorithm 🛠️

-Time Complexity: O(E log E)

-Space Complexity: O(V)

Concept: Finds the Minimum Spanning Tree (MST) of a graph by sorting edges.

6️⃣ Prim’s Algorithm 🌳

-Time Complexity: O(E log V)

-Space Complexity: O(V)

Concept: Constructs a Minimum Spanning Tree (MST) by adding the shortest edge.

🎨 Visualizations & Demonstrations

--Graph Traversals: Watch BFS and DFS algorithms explore graphs step-by-step.

--Shortest Path: Visualize how Dijkstra’s and Bellman-Ford find the shortest path in weighted graphs.

--Minimum Spanning Trees: Observe how Kruskal’s and Prim’s algorithms build MSTs by selecting edges with minimum weights.