Lambert here: For people who like to “connect the dots,” there is actually a mathematically grounded discipline that studies such networks (or graphs) formally. (For “node,” below, read “dot.”)
Matthew O. Jackson, William D. Eberle Professor of Economics, Stanford University, Brian Rogers, Associate Professor in the Department of Economics, Washington University, and Yves Zenou, Professor of Economics at Stockholm University and CEPR Research Fellow. Originally published at VoxEU.
There have been 24 outbreaks of the Ebola virus since it first appeared in 1976. Most were limited to dozens of cases, or at most hundreds – but the 2014 outbreak reached tens of thousands (Global Alert and Response, World Health Organization 2014). Although this latest outbreak now appears to be contained, the world may have dodged a dangerous bullet. If the disease had gotten a toehold in one of the many large urban slums throughout the world, the toll could have been dramatically larger. The same year saw an outbreak of measles in the US unlike any in decades, as a combination of complacency and fears of side effects led to lapses in vaccinations that allowed for susceptibility to contagion. Indeed, even small percentages of unvaccinated people – especially children – can lead small seeds of a very virulent disease to snowball into widespread infection.
The combination of world population growth and an increasingly interconnected society is producing new dynamics. Of course, deadly pandemics are not new. The Black Death (bubonic plague) wiped out tens of millions of people between the 14th and 19th centuries. Modern medicine and especially vaccinations have helped the world mitigate and even prevent many such catastrophes. But a changing world brings new challenges. Social distances between individuals currently average less than five degrees (Ugander et al. 2011) so that it is typically possible to go from one person via a friend to another friend, and another – and within five steps or so reach much of the rest of the world.
Historical data suggest that this closeness is indeed a modern phenomenon. For instance, using data from the spread of the bubonic plague, Marvel et al. (2013) estimate that in the Middle Ages average social distances between people were many times higher than they are today. The plague spread relatively slowly from one area to the next, taking four years to travel across Europe at a pace of less than a thousand kilometers per year, as people interacted mostly in limited local patterns. In contrast, modern travel means that a healthcare worker exposed to Ebola in a village in Sierra Leone can easily be in London or New York before showing symptoms. A child who catches measles in Anaheim, California can board a plane and bring it home thousands of miles away. Increased mobility combined with tightly clustered interactions (e.g. children in schools), mean that small pockets of vaccination lapses can generate heavy outbreaks. Limiting the terrible costs that can be imposed by contagious diseases including Ebola, measles, HIV, and many others, remains an important priority. What are the most effective ways to employ preventative measures, treatment for the ill, and barriers to contagion – including travel bans and the like? Properly addressing such questions requires understanding the complex networks of interactions that govern transmission, and a systematic framework for trading off the costs and benefits of policies.
Disease is but one example of diffusion through connections. As we have seen recently, despite the advantages of modern financial systems they are susceptible to systemic failures – a downturn in one country can lead to cascading downturns in others. In the EU the largest 50 or so banking institutions are now highly connected, with interbank exposures exceeding one trillion euros, more than their total Tier 1 capital (Alves et al. 2013). While disease and financial contagion share certain similarities, they differ in fundamental respects. Financial contagion is less well studied and the challenge of how to ‘vaccinate’ an institution without slowing the economy is significant. How can we identify which institutions are really ‘too connected to fail’? Which financial institutions require regulation and how should regulatory policy be guided? Should financial integration be encouraged or discouraged? Again, answering these questions necessitates a network-based approach.
The increasing connectedness of the world also has many benefits: it enhances trade, increases the efficiency of investment, spreads prosperity and education, and fosters peace. For example, despite the poverty that still exists in the world, and the continued political and military conflicts that we endure, the world has been an order of magnitude more peaceful over the past few decades. Jackson and Nei (2015) find that the number of wars per pair of countries has been more than ten times lower in the period since 1950 than from the period of 1820 through 1950 – a decrease that mirrors a growth in trade. Networks of trade and political alliances have become denser and more stable in the period since the Second World War. How can understanding patterns of trade, employment, and growth help us to better understand conflict and prevent wars, both interstate and civil?
Insights from network science are poised to enable great progress on the questions posed above, among others. In a recent paper (Jackson et al. 2015), we describe many such insights about how network patterns of interactions impact contagion, diffusion, learning, markets, and behaviour. We outline fundamental principles by distinguishing between:
- Macro/global/aggregate network characteristics, which include the overall density of connections in a network as well as segregation patterns between people with different characteristics, and
- Micro/local/individual characteristics, including measures such as the extent to which two people have friends in common, whether a person’s friends are connected to each other, and how central or influential is a specific node in a network.
Macro patterns of a network play primary roles in processes of diffusion, contagion, and social learning, as well as in determining the extent to which disparate norms or cultures can exist within a society. Beyond the straightforward observation that denser networks (i.e. those having more interactions per individual) promote contagion, there are other robust insights that emerge from examining macro patterns. For example, financial settings differ in essential ways from simple epidemiological settings – not only does increasing the connectedness of institutions enable greater contagion, it also diversifies the risks held by individual institutions. Thus, the most dangerous network patterns for financial networks tend to have an intermediate density, being connected enough to diffuse distress from one institution to another but sparse enough that many institutions are poorly diversified and at risk from a neighbor’s distress.
A second macro characteristic of a network, with many implications, is the extent of segregation or homophily (the tendency of individuals to associate with others who share common traits). Homophily concentrates interactions among subpopulations and so, for example, can allow a disease or behaviour to take root among a subgroup who interact intensely with each other, while that disease or behaviour would not take root if the population were evenly mixing. For example, if there are many children in the same place at the same time (e.g. Disneyland), even a small percentage of unvaccinated individuals is enough to help an epidemic take root. This can then spread among them given that some parents have recently worried more about side-effects of vaccinations than the diseases they protect against – leaving some schools with substantial pockets of unvaccinated students and again having tight interactions among similarly susceptible individuals. Beyond its effects on contagion, homophily can also enable very different customs and norms of behaviour to exist in different parts of a network, and thus plays a role in phenomena like persistent inequality and poverty traps among people of different ethnicities.
‘Micro’ patterns of a network, such as identifying central or influential nodes, are of crucial importance in understanding how, for example, to effectively seed a program or how best to avoid a contagion. The relevant notion of centrality or influence depends on the application, but there are many tractable and natural measures of network centrality. Some measures capture how important a node is as a connector – bridging different parts of a network and potentially serving as an intermediary. Other measures track how influential a node is in terms of influencing others’ behaviours, for instance in identifying ‘key players’ who are most influential in a criminal network. Yet other measures track how well-placed an individual is to initiate diffusion of a product or idea. Each such measure has an intuitive relationship to the network, and understanding the multitude of measures of social influence, and which ones have proven useful in which circumstances, can help in shaping many policies – from controlling disease, to improving economic development, to guiding financial bailouts.
As we discuss at length in Jackson, Rogers and Zenou (2015), network science is at an exciting juncture: the modern world increasingly demands a unified understanding of networks, and the science is rapidly developing to deliver easy-to-articulate principles and concepts that are proving useful.
References
Alves, I, S Ferrari, P Franchini, J Heam, P Jurca, S Langfield, F Liedorp, A Sanchez, S Tavolaro and G Vuillemey (2013), “The structure and resilience of the European interbank market,” European Systemic Risk Board (ESRB) Occasional Paper No. 3.
Jackson, M O, and S Nei (2015), “Networks of military alliances, wars, and international trade,” SSRN discussion paper 2389300.
Jackson, M O, Rogers, B W, and Y Zenou (2015), “The economic consequences of social network structure”, CEPR Discussion Paper 10406.
Marvel, S A, Martin, T, Doering, C R, Lusseau, D, and M E J Newman (2013), “The small-world effect is a modern phenomenon,” preprint: http://arxiv.org/abs/1310.2636.
Ugander, J, Karrer, B, Backstrom, L, and C Marlow (2011), “The anatomy of the Facebook social graph“, preprint: .
19 comments
Comments are closed.
The introduction of the internet has ushered in an almost overnight revolution in the connectivity of the global network, requiring that we change how we approach virtually everything we do. While jet travel enabled us to cover great physical distances quickly, it didn’t necessarily lead to significantly increased connectivity, assuming humans as the network endpoints. With the internet, a user can post a video on YouTube and reach hundreds of thousands in 24 hours, and a teen in Russia can use commercial software to steal data on 100 million Target customers. Countries have loosely defined borders and no armed forces offer protection from electronic invasions, or even attempt to, while the internet of things both amass increasing amounts of data while leaving us more vulnerable. Whether banking crises or cybercrime, the narrative has shifted from prevention to resilience.
The industrial revolution caused the shift from an agrarian to a fuel-based economy. The internet has ushered in a shift from a fuel-based to a data-driven economy. Disrupt the flow of ones and zeroes and the world shuts down. Forming public-private allegiances to address concerns over cybersecurity is naïve. Both Google and the NSA want sole control of information.
“Give me control of a nation’s data and I care not who makes it’s laws?” ~LL
Strictly speaking it can be possible to protect against “electronic invasion”, but that would require the digital equivalent of borders. In other terms, national firewalls.
Then again, first i would recommend ditching the system of non-national top level domains, that is .com and similar. When you access a .com, you can’t tell if you are in Chinese, US, Russian, or any other jurisdiction. This has lead to insanities like the US FBI confiscating the .com domain of a Spanish site.
One of the less-discussed aspects of measles is the evidence that the current vaccine is ineffective to a large extent, even with the multiple injection regimen. My kids never got measles. Luck? Herd immunity? Isolation from outbreaks?
I had the measles as a child, and supposedly have life-long immunity, but my mother swore that she got it again when we kids brought it home from school…
There isn’t a perfect solution, unless measles can be totally eliminated.
Most diseases afflicting humanity come to us via animals: HIV and ebola are just the most recent examples. Measles is supposedly manifested as distemper in dogs (I can’t recall if it’s the regular or the German measle). Smallpox may have indeed come from cows, and cowpox, being the genetic precursor, could provide immunity to the super-bug that formed when the species shift occurred.
Medicine is not perfected, and Mother Nature is a mother…with tremendous creativity and all the time and resources in the world at her command.
The key to health is PUBLIC Health. This makes Obamacare even more of a dead-end waste of resources than most discerning people think it is.
I’d like to recommend a book written by Albert-László Barabási, published about fifteen years ago, on the subject of networks, as based on graph theory. It is clear, detailed, and written for the intelligent layperson.
The new, 2014 edition, is Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life. The previous edition, which is probably in many public libraries, is Linked: The New Science of Networks.
Fungi can do amazing things to model networks, optimizing them more rapidly than humans.
Heather Barnett has a brief talk that demonstrates many of these here: https://www.youtube.com/watch?v=2UxGrde1NDA
One of my all-time favorites on this topic is Paul Stamets. I particularly like the presentation he gave at the Uplift conference in Australia in 2013, called “Solutions from the Underground”: http://permaculturenews.org/2013/09/27/paul-stamets-solutions-from-the-underground-video/
Paul Stamets is extraordinary (as long-time NC readers know).
Paul Stamets fans might enjoy this radio interview about his younger days, showing the possibilities that can emerge from unconventional backgrounds:
http://www.thestory.org/sites/default/files/public/audio/story/the_story_1097_paul_stamets_first.mp3
I read/heard that when modeling and testing the US electrical grid for robustness and vulnerabilities yielded key understandings.
It was found that having a few key nodes was MUCH more dangerous (i.e. less robust) than if there were a centralized network with 1 main hub. The most robust networks–quickest to recover from problems–had many hubs; they were highly decentralized, with many small nodes.
These understandings were apparently not applied. We continue to have an electric grid with the most vulnerable configuration–a few major hubs. (And none of the transformers are off-the-shelf, and take 2 or more years to make just one, and they’re made in Korea. . . More dimensions of vulnerability.)
Not sure that ‘trade’ has increased at all. What has increased are transfers within coroporate entities that are counted as trade, so if Caterpillar transfers production of some sub-component to China, and ships over some parts in the process, that’s ‘trade’ with China. Really it’s just the outsourcing of production to locations where labour is kept docile by state violence. A realistic definition of ‘really existing gloablisation.’
Linked is a great book on this subject!
There’s an insightful quote by John Muir:
It’s frustrating when people claim that a particular event is the real cause of another event. Usually, there are many real causes of any event, since our world and the universe are so interconnected. It’s easy to fall into the trap of believing that a particular event is the real cause of something — I know I’ve made that mistake many times.
The Dalai Lama made this same point about people when he participated on a financial forum about a year ago. He said every person has a bond that connects him to every other person. He went on to say this was why we needed to focus more on addressing poverty and inequality. He said we’ve become self-centered members of society who don’t realize that when one person falls, everyone is pulled down. When those at the bottom are given a boost, everyone gets a lift.
Why would a financial forum include a Buddhist monk? Is it because universal wisdoms don’t change when viewed from different contexts?
Reminded me of a related article by Charles Hugh Smith in February 2011 about the various nodes in the status quo network as he saw them at that time, and the network’s resilience and vulnerabilities:
http://www.oftwominds.com/blogfeb11/chart-statusquo-02-11.html
Much to consider, and this article further informs. Thanks, Lambert!
Net-neutrality except for fee-shifting corporate road-hogs is based on the original DARPA 1969 of independent nodes to survive local attacks. It more or less relies on John Nash’s non-cooperative game theory of every player can give its best shot. Proof by survival, and revealed preference. At present there is more access to stores of knowledge and empowerment for the Individual than any other time in history. What this juncture the authors refer to: “…and understanding the multitude of measures of social influence, and which ones have proven useful in which circumstances, can help in shaping many policies – from controlling disease, to improving economic development, to guiding financial bailouts.” has Nothing To Do with empowering the Individual but shaping policies top down by understanding social-influencing metrics via big data volunteered by the colonists.
The revolution will be just Tuning Out.Thanks for the network ride.
If I can overcome my visceral reaction (been trying to ever since it posted in the wee sunless hours in the U$ time zones) to this stunningly blatantly murky disingenuous … venal slop (no surprise at all that some Stanford White Male Thought Leader is a part of this authorial White Male Thought LeaderTriad):
Oh fuck, apologies for neglecting that stupid, pain and time spent better elsewhere taking, end blockquote html code:
If I can overcome my visceral reaction (been trying to ever since it posted in the wee sunless hours in the U$ time zones) to this stunningly blatantly murky disingenuous … venal slop (no surprise at all that some Stanford White Male Thought Leader is a part of this authorial White Male Thought LeaderTriad):
I might revisit.
No small wonder that many of the regular posters at Naked Capitalism who are getting quite sick and tired of the stunningly teeny number of Algorithmic Thought Ma$ters of the Univer$e, likely had the same visceral reaction to this slobber, and could not bring themselves to be a lone wolf human commenter with so very many reservations as to the above “message.”
No mention of the correspondent exponential and utter lack of connectedness with one’s physical neighbors when the lights perhaps go out? ey? … just for one huge DEBATE.
Interesting approach. It hinges a little bit on vague notions of what we mean by modern – are we talking the last 15 years, 50 years, 500.
But I think financial contagion is a new problem, or perhaps a new scale of an old problem, due to technical developments being misused and public policy encouraging that misuse. Quite simply, the personal computing revolution allows for fraud and gambling to happen on a massive and secretive scale. We don’t even really know fully how the federal government uses its enormous power, let alone the myriad actors in state and local governance and quasi private financial firms.
Just like the only true way to protect a power plant from Internet hacking is to not connect it to the Internet in the first place, the only true way to protect a financial network is to not have inter-connectedness. While natural persons get vaccines because we value individual life, legal persons should be encouraged to die at the first signs of trouble. If one company failing could infect another, neither company should exist.
Or in shorter form, commercial banking should be completely separate from investment banking, the FDIC should stop subsidizing rates for deposit insurance, and the hodge podge of government debt guarantees, like mortgages and higher ed, should end. Now that’s s stronger network.
What utterly (deliberate? Or just stunningly exclusive highly paid, white male academia IGNORANT?) vague, Bullshit, lamely attempting to masquerade as “wisdom” :
WRONG. That faux connectedness™, at this point, is only serving a teeny eeny minuscule handful of ‘humans[?]’ (predominately obscenely wealthy, male, and pale). Sorry, but since you three AUTHORS were rather vague as to time frames, I took it that you three pale male Economists! were speaking to the current FASCIST, Mult- National! Corporatized Algorithm$ of connectedness™ over 99.999999999999999 percent of Humans.
First of all, Peace?
Do I really need to provide links of that so named “connectedness” being the prime factor in the capacity to Drone [MURDER] entire neighborhoods?
Secondly, care to comment on the ever exponentially increasing U$ (the U$ being a major “Home” to all that delightful [UNDESIRED/UNSOLICITED by most, OVERLOAD of SURVEILLING – ANT FARM STUDY TERRITORY] Connectivity! ™) MORTALITY RATE (particularly SUICIDES ACROSS THE SPECTRUM OF HUMANITY residing in the U$)? A Mortality Rate which appears to possibly be related to an overflow of undesired/unsolicited Connectivity! ™.
and yeah, uh, care to comment as to why that mortality rate likely graphs out on that same x and y axis line as your rate of (insinuated as net Primo ‘benevolence!’) Connectivity! ™?
The fact that land line telephones were likely the most significant (and far more, to this day, legally protected than Skype, et al, and mobile/i/android, et al phones) progress ever, regarding connecting and communicating – along with the fact that THOSE LANDLINE TELEPHONE OPTIONS are in the process of being rapidly and utterly destroyed, for 99.999999999999 percent of the population – informs my above comment.