Graphs are a fundamental data structure in computer science and mathematics, often used to model networks and relationships. In this section, we'll explore the basics of graphs, their types, and their applications.
Types of Graphs
Undirected Graphs 📈
- Nodes are connected to each other with no direction.
- Example: Social networks, road networks.
Directed Graphs (Digraphs) 📊
- Nodes are connected with a direction, indicating a relationship.
- Example: Flight networks, social media connections.
Weighted Graphs 🔎
- Edges have weights, representing some form of cost or distance.
- Example: Network routing, transportation networks.
Cyclic Graphs (Circular Graphs) 🌀
- Graphs with at least one cycle.
- Example: A cycle in a road network.
Acyclic Graphs (Non-Cyclic Graphs) 🔄
- Graphs without any cycles.
- Example: Hierarchical structures, family trees.
Common Graph Algorithms
Breadth-First Search (BFS) 🔍
- Explores the graph level by level, starting from a given node.
- More on BFS.
Depth-First Search (DFS) 🚀
- Explores the graph as deeply as possible before backtracking.
- More on DFS.
Dijkstra's Algorithm 🎯
- Finds the shortest path from a starting node to all other nodes in a weighted graph.
- More on Dijkstra's Algorithm.
Floyd-Warshall Algorithm 🔗
- Computes shortest paths between all pairs of nodes in a weighted graph.
- More on Floyd-Warshall Algorithm.
Kruskal's Algorithm 🔧
- Finds a minimum spanning tree for a connected weighted graph.
- More on Kruskal's Algorithm.
Applications
Graphs have a wide range of applications in various fields, including:
- Network Routing 🚀
- Social Networks 🤝
- Web Search 🌐
- Data Analysis 📊
- Artificial Intelligence 🤖
For more information on graph algorithms and their applications, visit our algorithms page.