1. CS 440 Database Management Systems
Graph Data & PageRank

2. How the Web different from a database of documents?

3. How the Web different from a database of documents?
Hypertext vs. text: a lot of additional clues
graph vs. set
anchor text vs. text: how others say about you?
Geographically distributed vs. centralized
so you need to build a crawler
Precision more valued than recall
quality is important than quantity, especially “broad” queries
Spamming
Hoaxes and more …

4. Web data and query Answer Basic data/query model Data model
directed graph
nodes: Web pages
links: hyperlinks
all nodes belong to the same type.
Query is a set of terms
Answer
ranked list of relevant and important pages
quantifying a subjective quality
Basic data/query model
more complex models, e.g., assigning types to pages.

5. Web search before Google
Web as a set of documents
Relevance: content-based retrieval
documents match queries by contents
q: ’clinton’  rank higher pages with more ‘clinton’
Importance???
contents: what documents say about themselves
many spams and unreliable information in the results.
Directory services were used
Yahoo! was one of the leaders
Google co-founders were told “nobody will use a keyword interface”.

6. Google: PageRank From the Stanford Digital Libraries project 1996-98
Published the paper in 1997:
S. Brin, L. Page: The Anatomy of a Large-Scale Hypertextual Web Search
Engine. WWW7 / Computer Networks 30(1-7): (1998)
Tried to sell to Infoseek in 1997
Founded in 1998 by Brin and Page

7. Web: Adjacent Matrix Web: G = {V, E} x y z V = {x, y, z}, |V| = n
E = {(x, x), (x, y), (x, z),
(y, z),
(z, x), (z, y) }
A: n x n matrix: Aij = 1 if page i links to page j, 0 if not
target node x y
A =
source node z

8. Transposed Adjacent Matrix
Adjacent matrix A:
what does row j represent?
Transpose At:
A =
row j in A: what nodes does node-j link to?
row j in At: what nodes links to node-j? x y
At = z

9. PageRank: importance of pages
PageRank (or importance): recursively
a page P is important if important pages link to it
importance of P:
proportionally contributed by the back-linked pages
Example:
vx = 1/2 vx + 1/2 vz
vy = 1/2 vz
vz = 1/2 vx + 1 vy
Random-surfer interpretation:
surfer randomly follows links to navigate
PageRank = the prob. that surfer will visit the page x y z

10. Computing PageRank Importance-propagation equation:
Computation: by relaxation
linked-from (At) or links-to matrix (A)?
column-normalized:
column x is all that x points to
sum of column = 1
Transition Matrix
1/ /2
v= /2 v 1/ v:
fixpoint
/4 … 6/5
1 1/2 3/4 … 3/5
1 3/ … 6/5 x y
linked-from matrix: since importance comes from the “source” nodes to the target nodes
sum of column = 1, since the source node distributes its importance to all the nodes that it links to z

11. Problems: Dead Ends x y a b z Dead ends: Example:
page without successors has nowhere to send its importance
eventually, what would happen to v?
Example:
va = 0 va + 0 vb
vb = 1 va + 0 vb x y a b z

12. Problems: Spider Trap x y a b z Spider traps: Example: Solutions??
group of pages without out-of-group links will trap a spider inside
what would happen to v?
Example:
va = 1/2 va + 0 vb
vb = 1/2 va + 1 vb
Solutions?? x y a b z

13. Solutions: surfer’s random jump
Surfer can randomly jump to a new page
without following links
M: transition matrix, e: a vector with all 1’s,
n: number of nodes in the graph
d: damping factor (set to .85 in paper)
model the probability of randomly jumping to this page
another interpretation:
“tax” importance of each page and distribute to all pages
Teleportation
v = d M v + (1-d) e / n
PR(A): PageRank of page A
T1, ... Tn: pages point to A; C(Ti): out degree of Ti (# of outlinks)

14. Anti-Spamming Spamming: Google anti-spam device:
attempt to create artifacts to “please” search engines
so that ranking will be high
e.g., commercial “search engine optimization service”
Google anti-spam device:
unlike other search engines, tends to believe what others say about you
by links and anchor texts
recursive importance also works:
importance (not just links) propagate
Still, not perfect solution

15. What you should know Web data and query model
PageRank formula and algorithm
Dead ends and spider traps
Teleportation