Graphs are a fundamental data structure used in computer science to model pairwise relations between objects. A graph consists of nodes (also called vertices) and edges that connect pairs of nodes. In this tutorial, we will explore the basics of graphs, including their types, properties, and algorithms.
Types of Graphs
- Directed Graphs: Edges have a direction, indicating the start and end points.
- Undirected Graphs: Edges have no direction, and the connections between nodes are bidirectional.
- Weighted Graphs: Edges have weights that represent some form of cost or distance.
- Unweighted Graphs: Edges have no weights.
Properties of Graphs
- Degree of a Vertex: The number of edges connected to a vertex.
- Degree Sequence: The sequence of degrees of all vertices in a graph.
- Path: A sequence of vertices connected by edges.
- Cycle: A path that starts and ends at the same vertex.
- Tree: A connected graph with no cycles.
Graph Algorithms
- Breadth-First Search (BFS): An algorithm to traverse a graph level by level.
- Depth-First Search (DFS): An algorithm to traverse a graph as deeply as possible.
- Dijkstra's Algorithm: An algorithm to find the shortest path between two vertices in a weighted graph.
- Floyd-Warshall Algorithm: An algorithm to find the shortest paths between all pairs of vertices in a weighted graph.
Graph Example
For more information on graph algorithms, you can read our detailed tutorial on Graph Algorithms.
Conclusion
Graphs are a powerful tool for modeling relationships and dependencies between objects. By understanding the different types of graphs and their properties, you can apply them to solve a wide range of problems in computer science and beyond.