Complexiteit de rol van netwerken (1) Uwe Matzat

www.tue-tm.org/complexity

Drie thema’s

Opzet Veel voorbeelden uit de sociale netwerk hoek Mede: aanloop voor volgende netwerkcollege over biologische netwerken (Soms slides in het Engels) umatzat _/at\_ gmail.com Several slides used from, e.g., Leskovec and Faloutsos , Carnegie Mellon, and others (see www.insna.org)

alles dat kan worden weergegeven en geinterpreteerd als Netwerken: alles dat kan worden weergegeven en geinterpreteerd als bolletjes met lijntjes daartussen

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 Include/dependency graph Language network Software network

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 Technological networks: Power grid Airline, road, river networks Telephone networks Internet Autonomous systems Florence families Karate club network Karate: 34 members, 2 years, disagreements between instructor and club administrator, the club split into two Friendship network Collaboration network

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)

Netwerken en complexiteit Karakteristieke kenmerken complexe systemen Groot aantal componenten Veelvoud van interacties De interacties tussen de componenten zijn sterk niet-lineair Zelforganiserend Adaptief Robuust  Fragiel

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)

De structuur van de omgeving doet er toe, niet alleen de eigenschappen van de elementen zelf “Bottom up” voorbeelden

Network analysis in HIV/AIDS research dataverzameling?

An example in crime: 9-11 Hijackers Network SOURCE: Valdis Krebs http://www.orgnet.com/

Dit is een wetenschap

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

SNA needs dedicated software (for data collection, data analysis and visualization) http://www.insna.org/software/software_old.html

Twee klassieke studies in de sociale netwerktheorie

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”.

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

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 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

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

Ron Burt: Structural holes versus network closure as social capital (2) 1 B 7 3 2 James Robert 6 4 5 9 8 C Robert’s network is rich in structural holes James' network has fewer structural holes D

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

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

“Top down” voorbeelden (kijk naar bestaande netwerken en probeer daar iets van te leren) Six degrees of separation & The small world phenomenon

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”

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

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.

What kind of structures do empirical networks have What kind of structures do empirical networks have? (often small-world, and often also scale-free)

3 important network properties Average Path Length (APL) (<l>) 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:

We find small average path lengths in all kinds of places… Power grid network of Western States 5,000 power plants with high-voltage lines  small APL

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.

APL is small in random networks [Slide copied from Jari_Chennai2010.pdf]

[Slide copied from Jari_Chennai2010.pdf]

But let’s move on to the second network characteristic …

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

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)

Example of interesting properties of small world networks

Combining game theory and networks – Axelrod (1980), Watts & Strogatz (1998?) Consider a given network. All connected actors play the repeated Prisoner’s Dilemma for some rounds 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 Repeat 2 and 3 until a stable state is reached. Conclusion: to sustain cooperation, you need a short average distance, and cliquishness (“small worlds”)

If small-world networks are so interesting and we see them everywhere, how do they arise? (potential answer: through random rewiring of given structures)

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?

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

And now the third characteristic

Same thing … we see “scale-freeness” all over

… and it can’t be based on an ER-network

Another BIG question: How do scale free networks arise? Potential answer: Perhaps through “preferential attachment”

Netwerken kunnen leiden tot niet-lineariteiten (en dat is mooi en lastig tegelijk)

: “are being eaten by”

Wat zal er gebeuren als Duitsland minder aan de US gaat leveren?

“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 zer Remember week 2? Kleine verschillen in het begin= grote verschillen op het eind * Watts, D.J. (2002) A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences USA 99, 5766-5771

Definities die we volgende keer nodig hebben

Social network basics – let’s 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”)

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

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)    

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)

Basic network measurements ... To be continued with biological networks