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Complexiteit de rol van netwerken (1) Chris Snijders www.tue-tm.org/complexity Chris Snijders – Complexiteit: Netwerken (1) 2 Networks of the Real-world (1) Biological networks metabolic networks food web neural networks gene regulatory networks Language networks Yeast protein interactions Semantic network Semantic networks Software networks … Language network Software network Chris Snijders – Complexiteit: Netwerken (1) Networks of the Real-world (2) Information networks: Social networks: people + interactions World Wide Web: hyperlinks Citation networks Blog networks Organizational networks Communication networks Collaboration networks Sexual networks Collaboration networks Florence families Karate club network Technological networks: Power grid Airline, road, river networks Telephone networks Internet Autonomous systems Friendship network Collaboration network 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) 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) 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” Chris Snijders – Complexiteit: Netwerken (1) 7 Netwerken leiden tot non-lineariteiten (en dat maakt alles lastig) Chris Snijders – Complexiteit: Netwerken (1) 8 Chris Snijders – Complexiteit: Netwerken (1) De structuur van de omgeving doet er toe, niet alleen de eigenschappen van de elementen zelf “Bottom up” voorbeelden Chris Snijders – Complexiteit: Netwerken (1) 10 Network analysis in HIV/AIDS research dataverzameling? Chris Snijders – Complexiteit: Netwerken (1) 11 An example in crime: 9-11 Hijackers Network SOURCE: Valdis Krebs http://www.orgnet.com/ Chris Snijders – Complexiteit: Netwerken (1) (Sept ‘09 on SOCNET list) Chris Snijders – Complexiteit: Netwerken (1) Chris Snijders – Complexiteit: Netwerken (1) 14 Chris Snijders – Complexiteit: Netwerken (1) 15 It's a science ... www.insna.org Chris Snijders – Complexiteit: Netwerken (1) SNA needs dedicated software (for data collection, data analysis and visualization) http://www.insna. org/software/soft ware_old.html Chris Snijders – Complexiteit: Netwerken (1) 17 Twee klassieke studies in de sociale netwerktheorie Chris Snijders – Complexiteit: Netwerken (1) 18 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”. Chris Snijders – Complexiteit: Netwerken (1) 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 Chris Snijders – Complexiteit: Netwerken (1) 20 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 Chris Snijders – Complexiteit: Netwerken (1) 21 Ron Burt: Structural holes versus network closure as social capital structural holes beat network closure when it comes to predicting which actor performs best University of Chicago, Graduate School of Business Chris Snijders – Complexiteit: Netwerken (1) Ron Burt: Structural holes versus network closure as social capital (2) A B 1 7 3 2 James 6 Robert 5 C Robert’s network is rich in structural holes James' network has fewer structural holes 4 9 8 D 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 Chris Snijders – Complexiteit: Netwerken (1) 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 Chris Snijders – Complexiteit: Netwerken (1) 25 “Top down” voorbeelden Six degrees of separation & The small world phenomenon Chris Snijders – Complexiteit: Netwerken (1) 26 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” Chris Snijders – Complexiteit: Netwerken (1) 27 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 Chris Snijders – Complexiteit: Netwerken (1) 28 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. Chris Snijders – Complexiteit: Netwerken (1) The Kevin Bacon experiment – Tjaden (+/- 1996) Actors = actors Ties = “has played in a movie with” Chris Snijders – Complexiteit: Netwerken (1) 30 The Kevin Bacon game Can be played at: http://oracleofbacon.org Kevin Bacon number (data might have changed by now) Jack Nicholson: Robert de Niro: Rutger Hauer (NL): Famke Janssen (NL): Bruce Willis: Kl.M. Brandauer (AU): Arn. Schwarzenegger: 1 1 2 2 2 2 2 (A few good men) (Sleepers) [Jackie Burroughs] [Donna Goodhand] [David Hayman] [Robert Redford] [Kevin Pollak] Chris Snijders – Complexiteit: Netwerken (1) A search for high Kevin Bacon numbers… 3 2 Chris Snijders – Complexiteit: Netwerken (1) Bacon / Hauer / Connery (numbers now changed a bit) Chris Snijders – Complexiteit: Netwerken (1) The best centers… (2009) (Kevin Bacon at place 507) (Rutger Hauer at place 48) Chris Snijders – Complexiteit: Netwerken (1) “Elvis has left the building …” Chris Snijders – Complexiteit: Netwerken (1) “Small world networks” - short average distance between pairs … - … but relatively high “cliquishness” Chris Snijders – Complexiteit: Netwerken (1) We find small world networks in all kinds of places… Caenorhabditis Elegans 959 cells Genome sequenced 1998 Nervous system mapped small world network Power grid network of Western States 5,000 power plants with high-voltage lines small world network Chris Snijders – Complexiteit: Netwerken (1) 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? Chris Snijders – Complexiteit: Netwerken (1) Strogatz and Watts (2) “We move in tight circles yet we are all bound together by remarkably short chains” (Strogatz, 2003) Chris Snijders – Complexiteit: Netwerken (1) Small world networks are (often) “scale free” (not necessarily vice versa) Chris Snijders – Complexiteit: Netwerken (1) Find the underlying DYNAMICS that match the found STRUCTURE Scientists are trying to connect the structural properties … Scale-free, small-world, locally clustered, bow-tie, hubs and authorities, communities, bipartite cores, network motifs, highly optimized tolerance … to the processes that might generate them (Erdos-Renyi) Random graphs, Exponential random graphs, Smallworld model, Preferential attachment, Edge copying model, Community guided attachment, Forest fire models, Kronecker graphs Chris Snijders – Complexiteit: Netwerken (1) 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 Chris Snijders – Complexiteit: Netwerken (1) 42 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 Chris Snijders – Complexiteit: Netwerken (1) 43 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 Chris Snijders – Complexiteit: Netwerken (1) 44 Social network basics Networks consists of dots and lines (or arrows) between the dots Dots=nodes=objects=vertices Lines=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 Chris Snijders – Complexiteit: Netwerken (1) 45 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) Chris Snijders – Complexiteit: Netwerken (1) 46 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) Chris Snijders – Complexiteit: Netwerken (1)