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6.207/14.15: Networks
Lecture 7: Search on Networks: Navigation and Web
Search
Daron Acemoglu and Asu Ozdaglar
MIT
September 30, 2009
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Outline
Navigation (or decentralized search) in networks
Web search
Hubs and authorities: HITS algorithm
PageRank algorithm
Reading:
EK, Chapter 20.320.6 (navigation)
EK, Chapter 14 (web search)
(
Optional reading:
) “The SmallWorld Phenomenon: An Algorithmic
Perspective,” by Jon Kleinberg, in Proc. of ACM Symposium on
Theory of Computing, pp./ 163170, 2000.
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Networks: Lecture 7
Introduction
We have studied random graph models of network structure.
Static random graph models (Erd¨osRenyi model, conﬁguration model,
smallworld model)
Dynamic random graph models (preferential attachment model)
In the next two lectures, we will study processes taking place on networks.
In particular, we will focus on:
Navigation or decentralized search in networks
Web search: ranking web pages
Spread of epidemics
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Decentralized Search
Recall Milgram’s smallworld experiment, where the goal was to ﬁnd short
chains of acquaintances (short paths) linking arbitrary pairs of people in the
US.
A source person in Nebraska is asked to deliver a letter to a target
person in Massachusetts.
This will be done through a chain where each person forwards the
letter to someone he knows on a ﬁrstname basis.
Over many trials, the average number of intermediate steps in
successful chains was found to lie between 5 and 6, leading to
six
degrees of separation
principle.
Milgram’s experiment has two fundamentally surprising discoveries.
First is that such short paths
exist
in networks of acquaintances.
The smallworld model proposed by Watts and Strogatz (WS) was
aimed at capturing two fundamental properties of networks: short
paths and high clustering.
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Networks: Lecture 7
Decentralized Search
Second,
people are able to ﬁnd
the short paths to the designated target with
only local information about the network.
If everybody knows the global network structure or if we can “ﬂood the
network” (i.e., everyone will send the letter to all their friends), we
would be able to ﬁnd the short paths eﬃciently.
With local information, even if the social network has short paths, it is
not clear that such
decentralized search
will be able to ﬁnd them
eﬃciently.
Figure:
In myopic search, the current messageholder chooses the contact
that is closest to the target and forwards the message to it.
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A Model for Decentralized Search—1
Kleinberg introduces a simple framework that encapsulates the paradigm of
WS – rich in local connections with a few long range links.
The starting point is an
n
×
n
twodimensional grid with directed edges
(instead of an undirected ring).
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This note was uploaded on 04/17/2011 for the course ECONOMICS 14.14 taught by Professor Daronacemoglu during the Spring '11 term at MIT.
 Spring '11
 DaronAcemoglu

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