A web graph serves as a visual representation of the relationships among various web pages, analyzed using graph theory and algorithms.

In the realm of computer science and web development, a web graph is defined as a directed graph that illustrates the structure of a website or a segment of the World Wide Web. Each node within the graph symbolizes a web page, while each edge signifies a hyperlink connecting one page to another. This graphical representation is instrumental in understanding the structure and connectivity of the web, which is vital for numerous applications, including web search engines, web mining, and social network analysis.

The analysis of a web graph employs the principles of graph theory, a mathematical discipline dedicated to the study of graphs and their properties. Graph theory equips us with a variety of concepts and algorithms to measure different characteristics of a web graph, such as its size, density, diameter, and degree distribution. For instance, the size of a web graph is quantified by the total number of its nodes and edges, the density represents the ratio of existing edges to the total number of possible edges, the diameter is defined as the longest shortest path between any two nodes, and the degree distribution reflects the probability distribution of the degrees across the entire network.

In conjunction with graph theory, web graph analysis also utilizes algorithms to carry out specific tasks. These algorithms can facilitate operations such as searching for particular nodes or edges, determining the shortest path between two nodes, clustering nodes into groups, and ranking nodes based on their significance. A notable example is the PageRank algorithm, originally developed by Google, which ranks web pages based on the quantity and quality of incoming links.

Analyzing web graphs can yield valuable insights into the structure and dynamics of the web. It enhances our understanding of how information flows through the web, how web communities are formed and evolve, and how web pages can be optimized for search engines. Moreover, the methodologies and tools crafted for web graph analysis can be applied to various other types of networks, including social networks, biological networks, and transportation networks.