Complexiteit de rol van netwerken (1) Chris Snijders

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Complexiteitde rol van netwerken (1)Chris
Snijders
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www.tue-tm.org/complexity
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Opzet

• 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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Netwerken alles dat kan worden weergegeven en
geinterpreteerd als bolletjes met lijntjes
daartussen
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Networks of the Real-world (1)

• Biological networks
• metabolic networks
• food web
• neural networks
• gene regulatory networks
• Language networks
• Semantic networks
• Software networks

Semantic network
Yeast protein interactions
Language network
Software network
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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 network
Friendship network
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Netwerken en complexiteit

• (Sociale) Netwerken gaan over hoe de samenhang
  van elementen mede van belang is (en niet alleen
  de eigenschappen van de elementen)
• Het gedrag van netwerken kan typisch niet-lineair
  zijn, zelfs als de losse onderdelen lineair
  gedrag vertonen (? complexiteit)
• Grote netwerken ? complexiteit op basis van
  omvang van de berekeningen
• Netwerktheorie aanloop (voor volgende week)

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Twee manieren om iets van netwerken te begrijpen

• Bottom up (wat zou nu een goede positie in een
  netwerk zijn, of welke soort netwerken hebben
  goede of slechte eigenschappen)
• Top down (hoe zien de netwerken om ons heen er
  eigenlijk uit, en wat kunnen we daarvan leren
  over bijvoorbeeld hoe ze tot stand komen)

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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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Obesity as a networked concept
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(No Transcript)
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(No Transcript)
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The same goes for smoking
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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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Dit is een wetenschap
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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)

http//www.insna.org/software/software_old.html
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Twee klassieke studies in de sociale
netwerktheorie
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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)

• Granovetters 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)

• Lets 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
  ties
• 17 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 closure when it
  comes to predicting which employee performs best

University of Chicago, Graduate School of Business
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Ron Burt Structural holes versus network closure
as social capital (2)
A
B
1
7
3
2
James
Robert
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4
5
9
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C

• Roberts network is rich in structural holes
• James' network has fewer structural holes

D
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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 always 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 (kijk naar bestaande
netwerken en probeer daar iets van te leren) Six
degrees of separation The small world
phenomenon
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Milgrams (1967) original study

• Milgram sent packages to a couple hundred people
  in Nebraska and Kansas.
• Aim was get this package to ltaddress of person
  in Bostongt
• 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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Milgrams 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.colu
  mbia.edu)
• Email to ltaddressgt, 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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What kind of structures do empirical networks
have?(often small-world, and often also
scale-free)
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3 important network properties

• Average Path Length (APL) (ltlgt)
• Shortest path between two nodes i and j of a
  network, averaged across all pairs of nodes
• Clustering coefficient (cliquishness)
• The (average) probability that a two of my
  contacts are in contact with each other
• (Shape of the) degree distribution
• A distribution is scale free when P(k), the
  proportion of nodes with k connections follows

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The small world phenomenon Milgrams (1967)
original study

• Milgram sent packages to a couple hundred people
  in Nebraska and Kansas.
• Aim was get this package to ltaddress of person
  in Bostongt
• 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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Milgrams 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.colu
  mbia.edu)
• Email to ltaddressgt, 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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Ongoing Milgram follow-ups
6.6!
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The Kevin Bacon experiment Tjaden (/- 1996)

• Actors actors
• Ties has played in a movie with
• Small world networks
• short average distance between pairs
• but relatively high cliquishness

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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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2
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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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We find small average path lengths in all kinds
of places

• Caenorhabditis Elegans
• 959 cells
• Genome sequenced 1998
• Nervous system mapped
• ? small APL
• Power grid network of Western States
• 5,000 power plants with high-voltage lines
• ? small APL

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How weird is that?

• Consider a random network each pair of nodes is
  connected with a given probability p.
• This is called an Erdos-Renyi network.

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APL is small in random networks
Slide copied from Jari_Chennai2010.pdf
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Slide copied from Jari_Chennai2010.pdf
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But lets move on to the second network
characteristic
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(No Transcript)
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This is how small-world networks are defined

• A short Average Path Length and
• A high clustering coefficient
• and a random network does NOT lead to these
  small-world properties

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This is how small-world networks are defined

• A short Average Path Length and
• A high clustering coefficient
• and a random network does NOT lead to these
  small-world properties

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Small world networks so what?

• You see it a lot around us for instance in road
  maps, food chains, electric power grids,
  metabolite processing networks, neural networks,
  telephone call graphs and social influence
  networks ? may be useful to study them
• They seem to be useful for a lot
• of things, and there are reasons
• to believe they might be useful
• for innovation purposes (and hence
• we might want to create them)

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Examples of interestingproperties of small
world networks
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Combining game theory and networks Axelrod
(1980), Watts Strogatz (1998?)

1. Consider a given network.
2. All connected actors play the repeated Prisoners
   Dilemma for some rounds
3. After a given number of rounds, the strategies
   reproduce in the sense that the proportion of
   the more succesful strategies increases in the
   network, whereas the less succesful strategies
   decrease or die
4. Repeat 2 and 3 until a stable state is reached.
5. Conclusion to sustain cooperation, you need a
   short average distance, and cliquishness (small
   worlds)

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Synchronizing fireflies

• ltgo to NetLogogt
• Synchronization speed depends on small-world
  properties of the network
• ? Network characteristics important for
  integrating local nodes

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If small-world networks are so interesting and
we see them everywhere, how do they
arise?(potential answer through random
rewiring of given structures)
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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 starts at 0.75, decreases to zero
  (actually to 1 in 6 million)
• Strogatz and Wats asked what happens along the
  way with APL and Clustering?

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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)
? Implications for, for instance, research on the
spread of diseases...

• The general hint
• If networks start from relatively structured
• and tend to progress sort of randomly
• - then you might get small world networks a
  large part of the time

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And now the third characteristic
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Same thing we see scale-freeness all over
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and it cant be based on an ER-network
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Another BIG questionHow do scale free networks
arise?

• Potential answer Perhaps through preferential
  attachment
• lt show NetLogo simulation heregt
• Critique to this approach
• it ignores ties created by those in the network

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Netwerken kunnen leiden tot niet-lineariteiten
(en dat is mooi en lastig tegelijk)
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are being eaten by
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Wat zal er gebeuren als Duitsland minder aan de
US gaat leveren?
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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
• (randomly distributed)
• 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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Definities die we volgende keer nodig hebben
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Social network basics lets start to be more
formal about this

• A network (or graph) contains a set of actors (or
  nodes, objects, vertices), and a mapping of
  relations (or ties, or edges, connections)
  between the actors

1
2
For instance Actors persons Relationships
participates in the same course as
Or Actors organizations Relationships have
formed an alliance
(grafentheorie)
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Social network concepts ties

• Relationships can be directed
• Symmetrical by choice
• Symmetrical by definition
• (usually depicted as)

1
2
For instance person 1 likes person 2
1
2
Person 1 likes 2, 2 likes 1
1
2
Person 1 is married to 2
1
2
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Social network concepts weights

• Relationships can carry weights
• Actors can have a variety of properties
  associated with them

1
2
3
4
Actors persons Relationships know each other 3
and 4 know each other better (stronger tie)
?
?
?
?
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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 (for instance, average distance to
  others)
• Betweenness (how often are you on the path
  between i and j)
• 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 high
  cliquishness)