Case Study Of Webgraph
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The document discusses web graphs, where nodes represent web pages and edges represent hyperlinks. Web graphs are highly dynamic as pages and links are constantly added and removed. They also have properties like being sparse, with most pages having a constant number of links, and having small world characteristics, with the diameter being small relative to the graph's size. Analyzing web graphs can provide statistics about their structure and properties.
Case Study Of Webgraph
- 1. WEB GRAPHS
- 2. 2 Internet/Web as Graphs • Graph of the physical layer with routers , computers etc as nodes and physical connections as edges – It is limited – Does not capture the graphical connections associated with the information on the Internet • Web Graph where nodes represent web pages and edges are associated with hyperlinks
- 3. 3 Web Graph
- 4. 4 Web Graph Considerations • Edges can be directed or undirected • Graph is highly dynamic – Nodes and edges are added/deleted often – Content of existing nodes is also subject to change – Pages and hyperlinks created on the fly • Apart from primary connected component there are also smaller disconnected components
- 5. 5 Why the Web Graph? • Example of a large,dynamic and distributed graph • Possibly similar to other complex graphs in social, biological and other systems • Reflects how humans organize information (relevance, ranking) and their societies • Efficient navigation algorithms • Study behavior of users as they traverse the web graph (e-commerce)
- 6. 6 Statistics of Interest • Size and connectivity of the graph • Number of connected components • Distribution of pages per site • Distribution of incoming and outgoing connections per site • Average and maximal length of the shortest path between any two vertices (diameter)
- 7. 7 Properties of Web Graphs • Connectivity follows a power law distribution • The graph is sparse – |E| = O(n) or atleast o(n2 ) – Average number of hyperlinks per page roughly a constant • A small world graph
- 8. 8 Small World Networks • It is a ‘small world’ – Millions of people. Yet, separated by “six degrees” of acquaintance relationships – Popularized by Milgram’s famous experiment • Mathematically – Diameter of graph is small (log N) as compared to overall size • 3. Property seems interesting given ‘sparse’ nature of graph but … • This property is ‘natural’ in ‘pure’ random graphs
- 9. Conclusion The compression techniques are specializedspecialized for Web Graphs. The average link sizelink size decreases with the increase of the graph. The average link access timelink access time increases with the increase of the graph. 9
- 10. Conclusion The compression techniques are specializedspecialized for Web Graphs. The average link sizelink size decreases with the increase of the graph. The average link access timelink access time increases with the increase of the graph. 9