Graphs: Terminology Used in Graph Theory

Graphs are fundamental structures in computer science and mathematics, used to model relationships between objects. To understand graphs better, let's go over some key terminologies:

📌 Basic Terms

🔹 Graph (G): A set of vertices (V) and edges (E) represented as G = (V, E).
🔹 Vertex (Node): A fundamental unit in a graph, denoted as V.
🔹 Edge: A connection between two vertices, denoted as E.

📌 Types of Graphs

🔹 Directed Graph (Digraph): Edges have a direction, meaning connections go one way.
🔹 Undirected Graph: Edges do not have a direction, meaning connections are bidirectional.
🔹 Weighted Graph: Edges have weights representing costs, distances, or other values.
🔹 Unweighted Graph: All edges have equal significance (no weights).

📌 Graph Properties

🔹 Degree of a Vertex: The number of edges connected to a vertex.
🔹 Path: A sequence of edges connecting a series of vertices.
🔹 Cycle: A path that starts and ends at the same vertex without repetition.
🔹 Connected Graph: A graph where all vertices are connected.
🔹 Disconnected Graph: A graph with isolated vertices or components.
🔹 Acyclic Graph: A graph that does not contain cycles.
🔹 Tree: A connected, acyclic graph.

Understanding these terms is crucial for working with graph algorithms like BFS, DFS, Dijkstra's, and more. Graphs play a vital role in networking, social media, route planning, and many other fields.