Graph Theory in Coding Practice

Graph theory is a fundamental concept in computer science and algorithms. It is used to model various real-world problems, such as social networks, transportation systems, and more. Here are some key concepts and algorithms in graph theory.

Key Concepts

Vertex: A node or point in the graph.
Edge: A connection between two vertices.
Path: A sequence of vertices connected by edges.
Cycle: A path that starts and ends at the same vertex.
Tree: A connected acyclic graph.

Algorithms

Breadth-First Search (BFS): An algorithm to traverse or search the graph in a breadthward motion.
Depth-First Search (DFS): An algorithm to traverse or search the graph in a depthward motion.
Dijkstra's Algorithm: An algorithm for finding the shortest path between nodes in a graph.
Floyd-Warshall Algorithm: An algorithm for finding the shortest paths between all pairs of vertices in a weighted graph.

Example

To understand graph theory better, let's take a look at an example of a graph representing a social network.

graph LR
    A[You] --> B{Alice}
    B --> C{Bob}
    C --> D{Charlie}
    A --> E{David}
    E --> F{Eva}

In this graph, A is connected to B, B is connected to C, and so on.

Resources

For more information on graph theory, you can check out our Algorithms Overview page.