Network Science and the Web
Networked Life
CIS 112
Spring 2008
Prof. Michael Kearns
The 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 identification
Graph 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:
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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 indexed
Five 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 structure
Size of the Five
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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 sites
Diameter 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 complex
Degree 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?
Digression: “Collective Intelligence Foo Camp”@google
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Sponsored by O’Reilly publishers; interesting history
Interesting attendees:
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Interesting topics:
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Tim O’Reilly; Rod Brooks; Larry Page; many others
Lots of CI start-ups
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Web 2.0, Wikipedia, recommender systems
Prediction markets and corporate apps
How to design such systems?
How to “trick” people into working for “free”? (ESP Game and CAPTCHAs)
Decomposing more complex problems (see behavioral experiments to come)
Bad actors and malicious behavior
Ants
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 it
Hubs and Authorities
• Suppose we have a large collection of pages on some topic
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– 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 out
The 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 examples
The 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
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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 calculator
The “Random Surfer” Model
• Let’s suppose that E(p) sums to 1 (normalized)
• Then the resulting PageRank solution R(p) will
– also be normalized
– can be interpreted as a probability distribution
• R(p) is the stationary distribution of the following process:
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starting from some random page, just keep following random links
if stuck in a loop, jump to a random page drawn according to E(p)
so surfer periodically gets “bored” and jumps to a new page
E(p) can thus be personalized for each surfer
• An important component of Google’s search criteria
But What About Content?
• PageRank and Hubs & Authorities
– both based purely on link structure
– often applied to an pre-computed set of pages filtered for content
• So how do (say) search engines do this filtering?
• This is the domain of information retrieval
Basics of Information Retrieval
• Represent a document as a “bag of words”:
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for each word in the English language, count number of occurences
so d[i] is the number of times the i-th word appears in the document
usually ignore common words (the, and, of, etc.)
usually do some stemming (e.g. “washed”  “wash”)
vectors are very long (~100Ks) but very sparse
need some special representation exploiting sparseness
• Note all that we ignore or throw away:
– the order in which the words appear
– the grammatical structure of sentences (parsing)
– the sense in which a word is used
• firing a gun or firing an employee
– and much, much more…
Bag of Words Document Comparison
• View documents as vectors in a very high-dimensional space
• Can now import geometry and linear algebra concepts
• Similarity between documents d and e:
– S d[i]*e[i] over all words i
– may normalize d and e first
– this is their projection onto each other
• Improve by using TF/IDF weighting of words:
– term frequency --- how frequent is the word in this document?
– inverse document frequency --- how frequent in all documents?
– give high weight to words with high TF and low IDF
• Search engines:
– view the query as just another “document”
– look for similar documents via above
Looking Ahead: Left Side vs. Right Side
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So far we are discussing the “left hand” search results on Google
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“Right hand” or “sponsored” search: paid advertisements in a formal market
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Same two types of search/results on Yahoo!, MSN,…
Common perception:
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But both sides are subject to “gaming” (strategic behavior)…
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… and perhaps to outright fraud
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More later…
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a.k.a “organic” search;
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We will spend a lecture on these markets later in the term
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organic results are “objective”, based on content, importance, etc.
sponsored results are subjective advertisements
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organic: invisible terms in the html, link farms and web spam, reverse engineering
sponsored: bidding behavior, “jamming”
optimization of each side has its own industry: SEO and SEM
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organic: typo squatting
sponsored: click fraud