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Complexiteit de rol van netwerken (1) Chris Snijders.

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Complexiteit de rol van netwerken (1) Chris Snijders
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Page 1: Complexiteit de rol van netwerken (1) Chris Snijders.

Complexiteit

de rol van netwerken (1)

Chris Snijders

Page 2: Complexiteit de rol van netwerken (1) Chris Snijders.

Chris Snijders – Complexiteit: Netwerken (1)

www.tue-tm.org/complexity

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Chris Snijders – Complexiteit: Netwerken (1)

Networks of the Real-world (1)

Biological networks metabolic networks food web neural networks gene regulatory networks

Language networks Semantic networks

Software networks

Yeast proteininteractions

Semantic network

Language networkSoftware network

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Chris Snijders – Complexiteit: Netwerken (1)

Networks of the Real-world (2)

Information networks: World Wide Web: hyperlinks Citation networks Blog networks

Social networks: people + interactions Organizational networks Communication networks Collaboration networks Sexual networks Collaboration networks

Technological networks: Power grid Airline, road, river networks Telephone networks Internet Autonomous systems

Florence families Karate club network

Collaboration networkFriendship network

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Chris Snijders – Complexiteit: Netwerken (1)

Gebruiksaanwijzing

Veel voorbeelden uit de sociale netwerk hoek

Mede: aanloop voor volgende netwerkcollege over biologische netwerken

(Soms slides in het Engels)

c.c.p.snijders _/at\_ gmail.com

Several slides used from, e.g., Leskovec and Faloutsos , Carnegie Mellon, and others (see

www.insna.org)

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Chris Snijders – Complexiteit: Netwerken (1)

Netwerken en complexiteit

Netwerken zijn een voorbeeld van hoe de samenhang van elementen mede van belang is (en niet alleen de eigenschappen van de elementen)

Het gedrag van een netwerken kan typisch niet-lineair zijn, zelfs als de onderdelen ‘lineair gedrag’ vertonen

Grote netwerken complexiteit op basis van omvang van de berekeningen

Netwerktheorie: aanloop (voor volgende week)

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Chris Snijders – Complexiteit: Netwerken (1)

Two approaches to network theory

Bottom up (let’s try to understand network characteristics and arguments)

Top down (let’s have a look at many networks, and try to deduce what is happening from the observations)as in “small world networks”

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Netwerken leiden tot non-lineariteiten (en dat maakt alles lastig)

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De structuur van de omgeving doet er toe, niet alleen de eigenschappen van de elementen zelf

“Bottom up” voorbeelden

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Network analysis in HIV/AIDS research

dataverzameling?

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An example in crime: 9-11 Hijackers Network

SOURCE: Valdis Krebs http://www.orgnet.com/

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(Sept ‘09 on SOCNET list)

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It's a science ... www.insna.org

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SNA needs dedicated software

(for data collection, data analysis and visualization)

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http://www.insna.org/software/software_old.html

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Twee klassieke studies in de sociale netwerktheorie

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Chris Snijders – Complexiteit: Netwerken (1)

Mark Granovetter: The strength of weak ties

Dept of Sociology, Harvard, “The strength of weak ties” (1973)

How do people find a new job?

interviewed 100 people who had changed jobs in the Boston area.

More than half found job through personal contacts (at odds with standard economics).

Those who found a job, found it more often through “weak ties”.

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M. Granovetter: The strength of weak ties (2)

Granovetter’s conjecture: strong ties are more likely to contain information you already know

According to Granovetter: you need a network that is low on transitivity

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M. Granovetter: The strength of weak ties (3)

Let’s try to understand this a bit better ...

Coser (1975) bridging weak ties: connections to groups outside own clique (+ cognitive flexibility, cope with heterogeneity of ties)

Empirical evidence

Granovetter (1974) 28% found job through weak ties17% found job through

strong ties Langlois (1977) result depends on kind of job Blau: added arguments about high status people connecting to a more

diverse set of people than low status people

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Ron Burt: Structural holes versus network closure as social capital

structural holes beat network closurewhen it comes to predicting which actorperforms best

University of Chicago, Graduate School of Business

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Ron Burt: Structural holes versus network closure as social capital (2)

Robert

A B

C

1

23

45

6

7

James

Robert’s network is rich in structural holes

James' network has fewer structural holes

89

D

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Chris Snijders – Complexiteit: Netwerken (1)

Ron Burt: Structural holes versus network closure as social capital (3)

Robert will do better than James, because of: informational benefits “tertius gaudens” (entrepreneur) Autonomy

It is not that clear (in this talk) what precisely constitutes a structural hole, but Burt does define two kinds of redundancy in a network:

Cohesion: two of your contacts have a close connection Structurally equivalent contacts: contacts who link to the same third

parties

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Four basic (“bottom up”) network arguments

Closure competitive advantage stems from managing risk; closed networks enhance communication and enforcement of sanctions

Brokerage competitive advantage stems from managing information access and control; networks that span structural holes provide the better opportunities

Contagion information is not a clear guide to behavior, so observable behavior of others is taken as a signal of proper behavior.

[1] contagion by cohesion: you imitate the behavior of those you are connected to[2] contagion by equivalence: you imitate the behavior of those others who are in a structurally equivalent position

Prominence information is not a clear guide to behavior, so the prominence of an individual or group is taken as a signal of quality

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“Top down” voorbeelden

Six degrees of separation

&

The small world phenomenon

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Milgram´s (1967) original study

Milgram sent packages to a couple hundred people in Nebraska and Kansas.

Aim was “get this package to <address of person in Boston>” Rule: only send this package to someone whom you know on a

first name basis. Try to make the chain as short as possible.

Result: average length of chain is only six “six degrees of separation”

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Milgram’s original study (2)

An urban myth?

Milgram used only part of the data, actually mainly the ones supporting his claim

Many packages did not end up at the Boston address

Follow up studies all small scale

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The small world phenomenon (cont.)

“Small world project” has been testing this assertion (not anymore, see http://smallworld.columbia.edu)

Email to <address>, otherwise same rules. Addresses were American college professor, Indian technology consultant, Estonian archival inspector, …

Conclusion: Low completion rate (384 out of 24,163 = 1.5%) Succesful chains more often through professional ties Succesful chains more often through weak ties (weak ties mentioned

about 10% more often) Chain size 5, 6 or 7.

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The Kevin Bacon experiment – Tjaden (+/- 1996)

Actors = actors

Ties = “has played in a movie with”

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The Kevin Bacon game

Can be played at:http://oracleofbacon.org

Kevin Bacon number (data might have changed by now)

Jack Nicholson: 1 (A few good men)

Robert de Niro: 1 (Sleepers)

Rutger Hauer (NL): 2 [Jackie Burroughs]

Famke Janssen (NL): 2 [Donna Goodhand]

Bruce Willis: 2 [David Hayman]

Kl.M. Brandauer (AU): 2 [Robert Redford]

Arn. Schwarzenegger: 2 [Kevin Pollak]

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A search for high Kevin Bacon numbers…

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Bacon / Hauer / Connery (numbers now changed a bit)

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The best centers… (2009)

(Kevin Bacon at place 507)(Rutger Hauer at place 48)

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“Elvis has left the building …”

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“Small world networks”

- short average distance between pairs …

- … but relatively high “cliquishness”

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We find small world networks in all kinds of places…

Caenorhabditis Elegans959 cellsGenome sequenced 1998Nervous system mapped small world network

Power grid network of Western States5,000 power plants with high-voltage lines small world network

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Strogatz and Watts

6 billion nodes on a circle Each connected to nearest 1,000 neighbors Start rewiring links randomly Calculate “average path length” and “clustering” as the

network starts to change Network changes from structured to random APL: starts at 3 million, decreases to 4 (!) Clustering: probability that two nodes linked to a common

node will be linked to each other (degree of overlap) Clustering: starts at 0.75, decreases to 1 in 6 million (=zero) Strogatz and Wats ask: what happens along the way?

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Strogatz and Watts (2) “We move in tight circles yet we are all bound together by remarkably short chains” (Strogatz, 2003)

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Small world networks are (often) “scale free” (not necessarily vice versa)

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Find the underlying DYNAMICS

that match the found STRUCTURE

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The BIG question:How do scale free (and: small world) networks arise?

Perhaps through “preferential attachment”

< show NetLogo simulation here>

Critique to this approach: it ignores ties created by those in the network

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One final example

“The tipping point” (Watts*)

Consider a network in which each node determines whether or not to adopt, based on what his direct connections do.

Nodes have different thresholds to adopt(random networks)

Question: when do you get cascades of adoption?

Answer: two phase transitions or tipping points: in sparse networks no cascades as networks get more dense, a sudden jump in the likelihood

of cascades as networks get more dense, the likelihood of cascades

decreases and suddenly goes to zero

* Watts, D.J. (2002) A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences USA 99, 5766-5771

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Open problems and related issues

Applications to Spread of diseases (AIDS, foot-and-mouth disease, computer

viruses), fashions, knowledge ...

Small-world / scale-free networks are: Robust to random problems/mistakes Vulnerable to selectively targeted attacks

Computability: SNA requires computer power, given larger networks

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Chris Snijders – Complexiteit: Netwerken (1)

Social network basics

Networks consists of dots and lines (or arrows) between the dots

Dots=nodes=objects=verticesLines=relations=ties=edges

You can have more than one kind of dots (e.g., man/women)

Relationships can have directions and weights

Mathematically, this can be presented as a (adjacency) matrix

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Basic network measurements (there are many more)

At the node level- indegree (number of connections to ego [sometimes proportional to size])- outdegree (number of connections going out from ego)- centrality- betweenness

At the network level- density (# relations / possible relations)- centrality- average path length - scale-free (distr. of degrees follows a power law)- small-world (low aver. path length and cliques)

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Chris Snijders – Complexiteit: Netwerken (1)

Netwerken en complexiteit

Netwerken zijn een voorbeeld van hoe de samenhang van elementen mede van belang is (en niet alleen de eigenschappen van de elementen)

Het gedrag van een netwerk als geheel kan typisch niet-lineair zijn, zelfs als de onderdelen ‘lineair gedrag’ vertonen

Grote netwerken complexiteit op basis van omvang van de berekeningen

Netwerktheorie: aanloop (voor volgende week)


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