What are the basic concepts of graph theory?

What are the basic concepts of graph theory?

Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. The basic concepts include vertices (or nodes), edges (connections between nodes), and various types of graphs like directed, undirected, weighted, and unweighted.

Can you explain what a directed graph is?

A directed graph, or digraph, is a graph where the edges have a direction. This means that each edge connects an ordered pair of vertices, indicating a one-way relationship. For example, if there's an edge from vertex A to vertex B, it doesn't imply that there's an edge from B to A.

What is the difference between a tree and a graph?

A tree is a special type of graph that is connected and acyclic, meaning it has no cycles. In contrast, a general graph can have cycles and may not be connected. Every tree is a graph, but not every graph is a tree.

How do you find the shortest path in a graph?

To find the shortest path in a graph, algorithms like Dijkstra's or the A* algorithm are commonly used. Dijkstra's algorithm works well for graphs with non-negative weights, while A* is useful for pathfinding and graph traversal.