Understanding Web as a Directed Graph
The World Wide Web is a vast network of interconnected web pages. To understand how these connections work, we can represent the web as a directed graph, also known as the web graph.
Definition
Directed graph
A collection of vertices (nodes) connected by edges (links) that have a specific direction.
In the context of the web:
- Vertices represent web pages.
- Edges represent hyperlinks that point from one web page to another.
Note
- The web graph is not a complete graph.
- This means that not every web page links to every other web page.
Key Characteristics of the Web Graph
- Directed Edges:
- Hyperlinks have a direction.
- If Page A links to Page B, there is a directed edge from A to B, but not necessarily from B to A.
- Sparsity:
- The web graph is sparse, meaning most web pages link to only a small subset of other pages.
- Scale:
- The web graph is massive, with billions of vertices and edges.
Why Represent the Web as a Directed Graph?
- Search Engines:
- Algorithms like PageRank use the web graph to determine the importance of web pages based on their link structure.
- Web Crawling:
- Crawlers use the web graph to navigate and index web pages efficiently.
- Network Analysis:
- Researchers study the web graph to understand connectivity, identify influential pages, and detect communities.
Example
Consider three web pages: A, B, and C.
- Page A links to B and C.
- Page B links to C.
- Page C links to A.
This can be represented as a directed graph:
- Vertices: A, B, C
- Edges: A → B, A → C, B → C, C → A
