What is a web graph and how is it analysed?

A web graph is a visual representation of the relationships between different web pages, analysed through graph theory and algorithms.

A web graph, in the context of computer science and web development, is a directed graph that represents the structure of a website or a part of the World Wide Web. Each node in the graph represents a web page, and each edge represents a hyperlink from one page to another. This graphical representation allows us to understand the structure and connectivity of the web, which is crucial for various applications such as web search engines, web mining, and social network analysis.

Analysing a web graph involves the use of graph theory, a branch of mathematics that studies graphs and their properties. Graph theory provides a set of concepts and algorithms that can be used to measure various aspects of a web graph, such as its size, density, diameter, and degree distribution. For example, the size of a web graph is the number of its nodes and edges, the density is the proportion of possible edges that actually exist, the diameter is the longest shortest path between any two nodes, and the degree distribution is the probability distribution of the degrees over the entire network.

In addition to graph theory, web graph analysis also involves the use of algorithms. These algorithms can be used to perform tasks such as searching for specific nodes or edges, finding the shortest path between two nodes, clustering nodes into groups, and ranking nodes based on their importance. For example, the PageRank algorithm, which was originally used by Google, ranks web pages based on the number and quality of links to them.

Web graph analysis can provide valuable insights into the structure and dynamics of the web. It can help us understand how information flows on the web, how web communities form and evolve, and how web pages can be optimised for search engines. Furthermore, the techniques and tools developed for web graph analysis can also be applied to other types of networks, such as social networks, biological networks, and transportation networks.