Network Science and the WebThe Web as NetworkGraph Structure in the Web [Broder et al. paper]Five Easy PiecesSize of the FiveDiameter MeasurementsDegree DistributionsBeyond Macroscopic StructureHubs and AuthoritiesThe HITS System (Hyperlink-Induced Topic Search)The PageRank AlgorithmThe “Random Surfer” ModelBut What About Content?Basics of Information RetrievalBag of Words Document ComparisonLooking Ahead: Left Side vs. Right SideNetwork Science and the WebNetworked LifeCSE 112Spring 2007Prof. Michael KearnsThe Web as Network•Consider the web as a network–vertices: individual (html) pages–edges: hyperlinks between pages–will view as both a directed and undirected graph•What is the structure of this network?–connected components–degree distributions–etc.•What does it say about the people building and using it?–page and link generation–visitation statistics•What are the algorithmic consequences?–web search–community identificationGraph Structure in the Web[Broder et al. paper]•Report on the results of two massive “web crawls”•Executed by AltaVista in May and October 1999•Details of the crawls:–automated script following hyperlinks (URLs) from pages found–large set of starting points collected over time–crawl implemented as breadth-first search–have to deal with webspam, infinite paths, timeouts, duplicates, etc.•May ’99 crawl:–200 million pages, 1.5 billion links•Oct ’99 crawl:–271 million pages, 2.1 billion links•Unaudited, self-reported Sep ’03 stats:–3 major search engines claim > 3 billion pages indexedFive Easy Pieces •Authors did two kinds of breadth-first search:–ignoring link direction  weak connectivity–only following forward links  strong connectivity•They then identify five different regions of the web:–strongly connected component (SCC):•can reach any page in SCC from any other in directed fashion–component IN:•can reach any page in SCC in directed fashion, but not reverse–component OUT:•can be reached from any page in SCC, but not reverse–component TENDRILS:•weakly connected to all of the above, but cannot reach SCC or be reached from SCC in directed fashion (e.g. pointed to by IN)–SCC+IN+OUT+TENDRILS form weakly connected component (WCC)–everything else is called DISC (disconnected from the above)–here is a visualization of this structureSize of the Five•SCC: ~56M pages, ~28%•IN: ~43M pages, ~ 21%•OUT: ~43M pages, ~21%•TENDRILS: ~44M pages, ~22%•DISC: ~17M pages, ~8%•WCC > 91% of the web --- the giant component•One interpretation of the pieces:–SCC: the heart of the web–IN: newer sites not yet discovered and linked to–OUT: “insular” pages like corporate web sitesDiameter Measurements•Directed worst-case diameter of the SCC:–at least 28•Directed worst-case diameter of IN  SCC  OUT:–at least 503•Over 75% of the time, there is no directed path between a random start and finish page in the WCC–when there is a directed path, average length is 16•Average undirected distance in the WCC is 7•Moral: –web is a “small world” when we ignore direction–otherwise the picture is more complexDegree Distributions•They are, of course, heavy-tailed•Power law distribution of component size –consistent with the Erdos-Renyi model•Undirected connectivity of web not reliant on “connectors”–what happens as we remove high-degree vertices?Beyond Macroscopic Structure•Such studies tell us the coarse overall structure of the web•Use and construction of the web are more fine-grained–people browse the web for certain information or topics–people build pages that link to related or “similar” pages•How do we quantify & analyze this more detailed structure?•We’ll examine two related examples:–Kleinberg’s hubs and authorities•automatic identification of “web communities” –PageRank•automatic identification of “important” pages•one of the main criteria used by Google–both rely mainly on the link structure of the web–both have an algorithm and a theory supporting itHubs and Authorities•Suppose we have a large collection of pages on some topic–possibly the results of a standard web search•Some of these pages are highly relevant, others not at all•How could we automatically identify the important ones?•What’s a good definition of importance?•Kleinberg’s idea: there are two kinds of important pages:–authorities: highly relevant pages–hubs: pages that point to lots of relevant pages•If you buy this definition, it further stands to reason that:–a good hub should point to lots of good authorities–a good authority should be pointed to by many good hubs–this logic is, of course, circular•We need some math and an algorithm to sort it outThe HITS System(Hyperlink-Induced Topic Search)•Given a user-supplied query Q:–assemble root set S of pages (e.g. first 200 pages by AltaVista)–grow S to base set T by adding all pages linked (undirected) to S–might bound number of links considered from each page in S•Now consider directed subgraph induced on just pages in T•For each page p in T, define its –hub weight h(p); initialize all to be 1–authority weight a(p); initialize all to be 1•Repeat “forever”:–a(p) := sum of h(q) over all pages q  p–h(p) := sum of a(q) over all pages p  q–renormalize all the weights•This algorithm will always converge!–weights computed related to eigenvectors of connectivity matrix–further substructure revealed by different eigenvectors•Here are some examplesThe PageRank Algorithm•Let’s define a measure of page importance we will call the rank•Notation: for any page p, let–N(p) be the number of forward links (pages p points to)–R(p) be the (to-be-defined) rank of p•Idea: important pages distribute importance over their forward links•So we might try defining–R(p) := sum of R(q)/N(q) over all pages q  p–can again define iterative algorithm for computing the R(p)–if it converges, solution again has an eigenvector interpretation–problem: cycles accumulate rank but never distribute it•The fix:–R(p) := [sum of R(q)/N(q) over all pages q  p] + E(p)–E(p) is some external or exogenous measure of importance–some technical details omitted here (e.g. normalization)•Let’s play with the PageRank calculatorThe “Random Surfer” Model•Let’s suppose that E(p) sums to 1