innovation in networks and alliance management small world networks
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Innovation in networks and alliance management Small world networks. Course aim. knowledge about concepts in network theory, and being able to apply that knowledge . The setup in some more detail. Network theory and background Introduction: what are they, why important … - PowerPoint PPT PresentationTRANSCRIPT
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Innovation in networks and alliance management
Small world networks
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Course aim
knowledge about concepts in network theory, and being able to apply that knowledge
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The setup in some more detail
Network theory and background
- Introduction: what are they, why important …- Network properties (and a bit on trust)- Four basic network arguments- Kinds of network data (collection)- Business networks
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Two approaches to network theory
Bottom up (let’s try to understand network characteristics and arguments)as in … “Four network arguments” by Matzat and in the trust topic that will follow later
Top down (let’s have a look at many networks, and try to deduce what is happening from what we see)as in “small world networks” (now)
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What kind of structures do networks have, empirically?
(what a weird question, actually)
Answer: often “small-world”,
and often also scale-free
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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”)Number of closed triplets / Total number of triplets (or: probability that two of my ties are connected)
(Shape of the) degree distributionA distribution is “scale free” when P(k), the proportion of nodes with degree k follows this formula, for some value of gamma:
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Example 1 - Small world networks
NOTE- Edge of network theory- Not fully understood yet …- … but interesting findings
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Enter: Stanley Milgram (1933-1984)
Remember him?
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The small world phenomenon – Milgram´s (1967) original study
Milgram sent packages to several (60? 160?) 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. Aim: try to make the chain as short as possible.
Result: average length of a 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 typically 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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Some Milgram follow-ups…
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6.6!
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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 [Nick Stahl]
Famke Janssen (NL): 2 [Nick Stahl]
Bruce Willis: 2 [Patrick Michael Strange]
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… (2011)
18(Kevin Bacon at place 444)(Rutger Hauer at place 43, J.Krabbé 867)
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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 average path lengths in all kinds of places… Caenorhabditis Elegans
959 cellsGenome sequenced 1998Nervous system mapped low average path length
+ cliquishness = small world network
Power grid network of Western States5,000 power plants with high-voltage lines low average path length +
cliquishness = small world network
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How weird is that?
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Could there be a simple explanation? 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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NB Erdos was a “Kevin Bacon” long before KevinBacon himself!|
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APL is small in random networks
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But let’s move on to the second network characteristic …
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This is how small-world networks are defined:
A short Average Path Length and
A high clustering coefficient
… and a randomly “grown” network does NOT lead to these small-world properties
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Networks of the Real-world (1) 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
Source: Leskovec & Faloutsos
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Networks of the Real-world (2)
Biological networks metabolic networks food web neural networks gene regulatory
networks Language networks
Semantic networks Software networks …
Yeast proteininteractions
Semantic network
Language network Software network
Source: Leskovec & Faloutsos
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And if we consider all three…
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… then we find this:
Wang & Chen (2003) Complex networks: Small-world, Scale-free and beyond
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The scale-free
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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 hencewe might want to create them)
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Examples of interestingproperties of
small world networks
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Synchronizing fireflies …
<go to NetLogo>
Synchronization speed depends on small-world properties of the network
Network characteristics important for “integrating local nodes”
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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 Prisoner’s 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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And another peculiarity ... Seems to be useful in “decentralized computing”
Imagine a ring of 1,000 lightbulbs Each is on or off Each bulb looks at three neighbors left and right... ... and decides somehow whether or not to switch to on or
off.
Question: how can we design a rule so that the network can tackle a given GLOBAL (binary) question, for instance the question whether most of the lightbulbs were initially on or off.
- As yet unsolved. Best rule gives 82 % correct.- But: on small-world networks, a simple majority rule gets 88% correct.
How can local knowledge be used to solve global problems?
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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 a given structure)
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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 Watts 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 can’t be based on an ER-network
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Scale-free networks are:
Robust to random problems/mistakes ... ... but vulnerable to selectively targeted attacks
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Another BIG question:How do scale free networks arise?
Potential answer: Perhaps through “preferential attachment”
< show NetLogo simulation here>
(Another) critique to this approach: it ignores ties created by those in the network
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Some related issues
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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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Malcolm Gladwell
(journalist/writer: wrote “Blink” and “The tipping point”
Duncan Watts
(scientist, Yahoo,Microsoft Research)
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Hmm ...
<try Netlogo Small Worlds>
We will see that you do not always end up with small worlds!
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The bigger picture
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The general approach … understandhow STRUCTURE can arise from underlying DYNAMICS
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 processes(Erdos-Renyi) Random graphs, Exponential
random graphs, Small-world model, Preferential attachment, Edge copying model, Community guided attachment, Forest fire models, Kronecker graphs, …
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More material on the website ...
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To Do:
Read and comprehend the papers on small world networks, scale-free networks (see website).
Think about applications of these results