Welcome to our session on Graph Algorithms Implementation. A large proportion of real-world problems, from social networking to routing applications, can be represented by graphs. Understanding and implementing graph algorithms is thus a key skill to have in your programming toolkit. In this lesson, we introduce and explore one of the most fundamental graph traversal algorithms — the Breadth-First Search (BFS).

Before we dive into BFS, let's take a moment to understand what a graph is. A graph is a data structure that consists of a set of vertices (or nodes) and a set of edges that connect pairs of vertices. Graphs can be directed or undirected, depending on whether the edges have a direction. They can also be weighted or unweighted, depending on whether the edges have associated weights.

In TypeScript, graphs can be effectively represented using an adjacency list with type annotations to ensure clarity and reliability. An adjacency list can be modeled using a Map where each key represents a vertex, and the associated value is an array of adjacent vertices. Here’s an example of how you might represent a simple graph in TypeScript:

In this example, vertex A is connected to vertices B and , vertex is connected to , , and , and so on.