Gossip: Identifying Central Individuals in a Social Network

April 26th, 2017

Because dynamics of networks depend on the small interactions between many components, networks are an important topic in complexity theory. Social networks describe individuals and their connections to one another. Professor of Economics at Stanford, Matthew O. Jackson is interested in how social network shape affects the flow of information on a network.

Stanford Complexity Group hosted a seminar entitled “Gossip: Identifying Central Individuals in a Social Network” by Matt Jackson on 3/13/2017. His talk focused on his research on microfinance efforts in a collection of rural south Indian villages. Advertising via means that might be more obvious in a Western context- for example via the internet or printed posters- are less effective in these villages, in part due to low literacy rates. Instead, more effective efforts of advertising the availability of these microfinance loans rely on person to person communication. Spreading information person to person over a social network relies on identifying who are the “most central” individuals in a social network. But what does it mean for an individual to be “central”? How do different measures of centrality lead to differences in the spread of information flow on the network?

Professor Jackson and his co-authors on the study simulated the flow of information over the social network structure from actual villages where the information spread from most “central” individuals and centrality was measured in different ways. “Degree centrality,” the number of edges a node has, was not particularly effective in identifying individuals who could spread information over the network. Identifying individuals by their eigenvector centrality was a more effective centrality measure for identifying good candidates to spread information over the network. Eigenvector centrality takes into account the first-degree connections of an individual, like degree centrality, but also considers the connectedness of the individual’s neighbors.

Eigenvector centrality, however, assumes that the probability of someone sharing information doesn’t decay with time. Thus, they developed a new model of centrality- diffusion centrality, which is parameterized by time.

Ultimately, the different measures of centrality rely on delineating the entire social network. In reality this would not be an effective strategy for a company to figure out how to best advertise their service (consider: a representative going door to door survey each family’s connectedness might as well advertise the service to each individual family. This quandary motivated another tool for measuring centrality- gossip. By asking few members of the community to identify who they had heard news about recently. They termed this measure of centrality “communication centrality”. Individuals with high “communication centrality” were often also those who were most central when centrality was defined by “diffusion centrality.”

Testing these theoretical results in a few dozen South Indian villages, Matt Jackson and collaborators considered the participation in microfinance when the loans were advertised to a few “central” individuals, using the different measures of centrality. While degree centrality did not have a high correlation with the percent of individuals participating in microfinance from a village, both “diffusion centrality” and “communication centrality” did.

While the results of these projects may be specific to microfinance in small villages, the question of how to spread helpful important information over a network extends to other types of social networks as well. Matt Jackson is also interested in studying the flow of information over larger web-based social networks, for example, how simple parenting tips like talking to babies from an early age, could effectively spread through social networks.

Matt Jackson’s work is a fascinating example of applying complexity theory to real world problems and we thank him for a wonderful seminar.

Discussion of “Racism 4.0, Civity, and Re-Constitution” by Palma Strand

October 14th, 2016

Next week, we will be hosting a visit by Palma Strand. In preparation for her seminar, we discussed Strand’s 2015 paper “Racism 4.0, Civity, and Re-Constitution”. The paper can be found here. This blog post is a summary of what we talked about. If you are curious about complexity and law, or perhaps “Applied Chaos Theory”, then read on…

First, we talked about the content of the paper and sketched out Strand’s framework. The overarching model in this paper is that we can think about the functioning of a nation in two parts: a “software” component (individual behavioral biases), which runs on a “hardware” component (structural & legal inequalities). Focusing on Blackness and Whiteness in the USA, Strand describes 4 iterations of the “operating system” of inequality. Racism 1.0 was the period of slavery, 2.0 was the post-slavery period of domestic terrorist acts such as lynching, 3.0 was typified by Jim Crow laws, and today we find ourselves in Racism 4.0. In today’s Racism 4.0, the overt manifestations of discrimination are nominally illegal (due to the Civil Rights legislature), yet we still have enormous social/economic inequality.

The main question is now: how do we proceed towards equality and justice? Strand suggests that the way forward should be guided by a pair of concepts: “Civity” and “Re-constitution”.

Civity” is a pragmatic sociological philosophy that addresses problems in the “software” branch of racism, for example by forming positive-valence interracial relationships. “Re-constitution” is a morally-imperative legal framework that addresses problems in the “hardware” branch, for example by directing housing organizations to normalize past patterns of housing inequality.

In the following image, the top branch is “software”, representing individual-level behavioral bias. This bias consists of pro-White & anti-Black components, and is addressed by Civity. The bottom branch is “hardware”, representing structural/legal inequality. This inequality consists of pro-White & anti-Black components, and is addressed by Re-constitution.


Civity is based on the creation of cross-cutting relationships. In the left side of the following image, a social network with mainly white nodes becomes tied to a social network with mainly blue nodes, after the creation of a strong link between the hubs. On the right, two smaller networks are not connected to each other, but each network is demographically admixed.


We saw several implicit and explicit parallels between Strand’s perspective on inequality and the Complex Adaptive System (CAS) framework. Points of harmony include:

  1. Non-linear emergent outcomes of a collective system. In society (as in other CAS systems), many distributed agents act on local information, generating system-level outcomes. The system-level outcome may be quite unpredictable from only knowing the agent-level rules, and vice-versa. This can be modeled with agent-based models.
  2. Path dependence. Strand discusses the role of past inequalities in current decision-making, for example in cases of affirmative action. Many CAS systems have a tremendously long memory of the environment. This is sometimes called “path-dependence”. For systems with high path-dependence, the response to a given stimulus is strongly contingent on the past experiences of the system.
  3. Network thinking. One manifestation of Civity is the restructuring of small-world social networks to include positive-valence interracial bridges between hubs. Many CAS systems are represented by networks, and network/graph theory is a long-time playground for CAS theory development.
  4. Anticipation. Many CAS systems do not passively react, they actively pre-act. For example, the pancrease starts to ecrete insulin when we see food, not when our blood sugar levels rise. Some CAS systems form models of the world around them, and act based upon predictions about the way the world works (Bayesian brain). On page 784 there is a nice discussion about how housing agencies can become more proactive to nip problems in the bud, instead of simply responding to crisis-level inequality. This cybernetic perspective on law might facilitate more effective treatments of social problems.
  5. Multiple spatial-temporal scales with feedback loops. Many CAS systems are integrated in behavior across multiple spatial scales. For example cells cooperate to generate tissue function, and tissues cooperate to generate organismal behavior. Other examples might include the relationships between local, state, and national government. Developmental complex systems are like embryonic Russian matryoshka dolls — hierarchically-structured dynamic matter, resplendent with feedback loops between scales, effortlessly giving rise to self-organized beauty.

After summarizing the main points of the paper and brainstorming points of harmony with CAS, we had a few open questions. To give two examples:

First, we wanted to learn more about how the many governmental scales of action can be synchronized for the good of the group. For example which equitable actions should be performed within Palo Alto, and which between East Palo Alto and Palo Alto? Which actions should include all of the Bay Area, California, or the country?

Second, we were inspired by the citations to a literature corpus that we were less-than-familiar with: non-quantitive perspectives on complexity. For example, there were citations about leadership complexity, organizational structure, and complexity in legislature. We wanted to know about the historical and current patterns of citation/idea-exchange between the quantitative and non-quantitative complexity literature.

All in all, it was a great paper and interesting discussion. Strand’s model is both pragmatic and normative about social justice. Without normativity, a social model is irrelevant  But without pragmatism, a social model is impractical. Thus Strand’s framework can serve the academic, but more importantly, aims for the service of the population.


Dr. W. Brian Arthur – Complexity and the Economy

March 3rd, 2016

Dr. W. Brian Arthur gave the 2015 Fall Complexity Seminar. His talk was titled Complexity and the Economy. Dr. Arthur spoke about the early days of this effort at SFI and explain how this new economics works and why it is needed. Complexity gives a view of the economy not as a perfectly balanced, smoothly functioning machine, but as a system that is organic, evolutionary, ever-changing, and historically-contingent.

Watch the video of his talk here:

Chris Adami Video

June 10th, 2015

Chris Adami gave the Spring Complexity Seminar. His talk was titled A New Approach to Intelligent Machines. In his talk he discussed why evolving intelligent machines will likely be more successful than current deep learning approaches, and argued that this approach will make machines that can actually think.

Watch the video of his talk here:

Between Dimensions at Stanford

April 24th, 2015

Last Saturday, Stanford Complexity Group brought an art installation to a Chi Theta Chi all-campus party. The installation, “Between Dimensions” creates hypnotic projections of fractal-like video feedback looping.


Party attendees interacting with “Between Dimensions”



“Between Dimensions” is a collaboration between Nathan Kandus, David Wright, Joel Thompson, Luke Wilson, Evan Glantz, and the Envelope Engineers. The project was originally created for Burning Man 2014 and is now being shown throughout the Bay Area. The installation was shown at the Exploratorium and will soon be shown at the California Academy of Sciences. One of the collaborators on the project, Joel Thompson, is a member of the Stanford Complexity Group who is on leave from his PhD to make art in Detroit, Michigan full time. Joel and Nathan’s vision for “Between Dimensions” is to make the understanding of complex systems accessible to everyone through the experience of observing them.

Nathan Kandus and his team set up “Between Dimensions”


A video feedback loop system, like “Between Dimensions”, is created by facing a camera at its monitor. Small visual noise introduced by the camera and the display becomes magnified and distorted over the iterative mapping from input to output. Video feedback loops can create colorful, intricate, moving patterns that appear mandala-like in their detail. The “Between Dimensions” projection also adds mirroring and can change the colorization. In addition, the installation has an interactive component that allows observers to rotate the camera or create shadows that multiply and twist with the rest of the image.

Projections from “Between Dimensions” on the wall of Chi Theta Chi

The title for the project, “Between Dimensions” refers to the fractional dimension of complex systems. The Cantor Set, an example of a fractal, is a set of intervals on (0,1) that is created by iteratively subsetting this interval into thirds and removing the center subset. It has a fractional dimension that is less than one but greater than zero. The Lorenz attractor has a fractional dimension between one and two. It appears two dimensional because the butterfly-like sides of the attractor are made up of infinitely close one dimensional curves. This fractional dimension is what defines fractal-like systems as somewhere between deterministic and stochastic.

“But why isn’t it deterministic? Couldn’t you know where any point would map to if you did the math?” asked one party-goer. Other students asked questions such as, “How does the system produce different colors?” or, “Why does it look like a kaleidoscope?”

Others simply marvelled at the psychedelic quality of the art.

Nathan and David explain video feedback to two students.

More party goers interact with “Between Dimensions”


This is the beauty of complex systems- that even without explanation, the patterns somehow fix our attention. The system both seems predictable at times, and isn’t. The understanding of the underlying intricacies seem just beyond our fingertips. It feels both ethereal and life-like. The experience leaves us awestruck.

Overall, Stanford Complexity Group believes this endeavor was extremely successful. We were happy to see many students interested to know more about complex systems and what the Stanford Complexity Group does. Almost all seemed to appreciate the art and many took stickers or wanted to join the listserv. We thank Nathan Kandus and his colleagues for bringing us Between Dimensions, and Chi Theta Chi for hosting the installation at their event, especially Matt Simon and Jonathan Colen for coordinating with us. We hope to do more events like this in the future.

Self Assembling Wires

February 8th, 2015

Check out this new video exploring a fascinating example of a self-organization created with only ball bearings, oil, and a high voltage source!




Swarms and CGI

November 14th, 2014

I was watching a Nature program the other day and a friend mentioned how disappointing it was to see computer generated imagery (CGI) on a nature program. I explained to him that in fact, everything in the nature program was real footage and none was computer generated. It is easy to explain why. CGI simply isn’t good enough at swarm behavior yet! Researchers have been working on getting computer generated agents to ‘look right’ for decades, and while the algorithms have gotten better, we aren’t quite there yet.

One of the first flocking algorithms was created by Craig Reynolds in 1986.

Since then, there have been great improvements, including this video of a crowd.

I’ve fallen, and I can’t get up! from Dave Fothergill vfx on Vimeo.

Some things still aren’t quite right. For some beautiful footage of real swarms, check out PBS’s nature program, Gathering Swarms.



Double Pendulum Simulation

October 17th, 2014

The double pendulum is a simple and elegant demonstration of a complex system. A single pendulum consists of a weight that is free to rotate about a fixed axis. Pendulums have been used since the 1600s in clocks. Pendulums swing back and forth with a constant time between each swing, that depends of the length of the pendulum, making them useful in time keeping.

A double pendulum is a system in which a single pendulum has a second single pendulum attached at the end of the first. Under certain conditions, such as small oscillations, the double pendulum can be just as consistent as the single pendulum, however under more extreme cases the double pendulum can behave erratically. What is interesting about the double pendulum is that it is a system of deterministic chaos. That is, for a given starting position, you can predict where the pendulum will be at some point in the future. However, even incredibly slight variations in the starting location can lead to very different positions only a short time later.

If you haven’t already, take a look at the Stanford Complexity Group’s double pendulum video, and then try the simulation below.

See if you can recreate the behaviors in the video. Can you make the single pendulum behave in a periodic way with both weights moving in the same direction? What about if the weights are moving in different directions? What kind of chaotic behavior can you get?



Double Pendulums

August 3rd, 2014

Double pendulums are a great example of chaos. Check out our video below to learn more!


Chaos in Media

July 28th, 2014

Michael Crichton’s Jurassic Park opens with Dr. Ian Malcom delivering a talk about chaos theory and dinosaurs at the Santa Fe Institute (SFI). SFI is a hub for complex systems research and a home to Ian Malcom, the man with bold plans for de-extinction . Fans of the novel (and the later movie) and reporters reached out to SFI to get in contact with Malcom. The only problem was that he only existed in Crichton’s book, not in real life. The fact that some students at SFI had created a webpage for Malcom hosted on SFI’s website only added to the confusion.

As chaos and complexity become more popular, the line between fact and fiction can become blurred. 


Image taken from xkcd