Welcome to our deep dive into Graphs, an essential data structure used in various real-world applications. This lesson is designed for both beginners and intermediate learners, so let's get started! š
A graph is a collection of nodes (also called vertices) and edges that represent connections between the nodes. Graphs are used to model complex relationships, such as social networks, road networks, and even the internet.
In a graph, nodes can represent entities like people, cities, or websites, and edges represent relationships like friendships, roads, or hyperlinks.
An undirected graph doesn't have a direction; if there's an edge between two nodes, it can be traversed in both directions.
A directed graph has a direction. An edge from node A to node B doesn't mean there's an edge from node B to node A.
A weighted graph assigns weights (or costs) to edges, which can represent distances, costs, or time.
A cyclic graph has at least one cycle (a sequence of edges and nodes where you can travel from a node back to itself), while an acyclic graph doesn't have any cycles.
Graphs can be represented in various ways, such as:
Let's consider a simple graph of some cities connected by roads.
Cities:
A
B
C
D
E
Edges:
A - B
A - C
B - D
C - D
C - EIn the adjacency list representation, each node is associated with a list of its neighboring nodes:
const graph = {
A: ['B', 'C'],
B: ['A', 'D'],
C: ['A', 'B', 'D', 'E'],
D: ['B', 'C'],
E: ['C'],
};In the next sections, we'll learn about important graph algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS).
What is a graph in simple terms?
What is an adjacency list in graph representation?