IFORS Conference

#NetworkScience

I was back in Barcelona this past week, for the 20th conference of the International Federation of Operational Research Societies (IFORS).  This triennial conference provides a forum for academics, practitioners, and software developers to exchange ideas throughout operations research.  The conference represented the incredible breadth of the field; topics included mathematical programming and optimization, simulation, transportation, military applications, health systems, finance, supply chains, and energy.  The next IFORS conference will be in Quebec City in 2017.

Talks on technology diffusion, military applications, health, and transportation particularly excited me, as they tie in with ongoing projects at the Network Science Center and other centers around West Point.  A talk on technology diffusion seems directly applicable to the ongoing entrepreneurial networks project at the Network Science Center.  Martin Zsifkovitz demonstrated an agent-based simulation approach to model how consumers adopt and purchase new products in the technological space.  Specifically, he modeled how technological innovations are adopted over time in a community through a social system, using consumer, producer, and government nodes.  This research will greatly inform the simulation and validation stage of the entrepreneurial networks project.  After policy recommendations are made via the comparison and optimization stages, discussed in an earlier blog post, we plan to implement agent-based simulation.  This framework will help us determine whether our recommendations would have the desired impact on the entrepreneurial ecosystem.

Two talks in the military applications space stood out.  One was on scheduling Canadian armed forces search and rescue response operations.  Bohdan Kaluzny applied integer programming techniques to schedule military personnel shifts.  His objective: minimize emergency response-time.  The other talk focused on terrain-dependent facility location, given by Andries Heyns.  He used military GIS data and multi-objective optimization techniques to place radar such that detection-range is maximized.  The same approach can be applied to minimize visibility of a particular deployed system, such as reconnaissance technology.  Many military applications demand that terrain-dependence is taken into account. For example, it might be impossible or cost-prohibitive to place a watchtower in a river.  Additionally, the layout of watchtowers in an open field would likely differ from the corresponding layout in a dense forest.

The health and transportation talks sparked an idea for the upcoming ungoverned spaces project at the Network Science Center, which investigates areas in which the government does not exercise effective sovereignty.  However, if the government is armed with greater logistics and health-delivery capabilities, it could potentially out-compete other groups for power, legitimacy, and support.  Eventually, the space might transform from ungoverned to governed.  While this is a broad and general idea, it provides an avenue for future research as the project develops.  One talk described a network model of ambulance stations, with the aim of minimizing emergency response-times.  Another talk also applied a network framework to minimize the transport-time of medical samples to hospital labs for testing.  Finally, another talk described synchronization in vehicle routing.  Many routing problems require vehicles of different types to meet at certain points.  Vehicles could exchange cargo or jointly perform some action at these locations.  I look forward to applying the techniques and research exposed to me at IFORS to ongoing and future projects at the Network Science Center.

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Hub Accra

On previous blogs, I have described visits to several tech hubs and incubators across the African Continent. I recently visited Accra, Ghana and previously wrote about a recent visit to the Meltwater Entrepreneurial School of Technology (MEST). This blog introduces another tech hub in the booming Accra Entrepreneurial Ecosystem, Hub Accra.

Hub Accra

After spending a few days with the staff and entrepreneurs at MEST, I had the opportunity to visit Hub Accra and interview a different group of entrepreneurs. Hub Accra is located on Klannaa Street in the booming and trendy Osu District of Accra. John-Paul Parmigiani, Hub Accra’s Chief Executive Officer, graciously hosted me during my visit.

Hub Accra in the Osu District of Accra

Hub Accra is a not-for-profit organization; they charge members modest fees for membership and also rent event space. John-Paul describes the hub as a “startup ecosystem.” The hub evolved out of a Certificate in Entrepreneurship Program offered by Open University of West Africa (OUWA). The Entrepreneurship Program attracted students from across Accra to study at OUWA’s Internet café campus, which is also located in Osu. These students met at the campus to access online lectures, and organically-formed teams to work on numerous group projects. Staff members of OUWA identified an opportunity and established Hub Accra.

Hub Accra has grown to host over 20 startups and quickly moved from normal operational hours to become Ghana’s first 24 hours, 7 days a week co-working space. John-Paul explained that many of the local entrepreneurs would come to the hub after school or after work, and this schedule resulted in requests for later operating hours.

Hub Accra is now housed in a separate building adjacent to OUWA, and features collaborative workspaces, internet access, and conference rooms. The second floor hosts space dedicated to the rapidly growing startups.

Over the course of the past year they have hosted numerous events, instituted programs, held workshops, brought in speakers, and established partners within the local community and across the world. During my visit, Hub Accra’s staff hosted a visit of MBA candidates from the University of Texas’ McCombs School of Business.

John-Paul Parmigiani, Hub Accra’s CEO briefing students from the McCombs School of Business at the University of Texas in Hub Accra’s main meeting room.

Educate, Incubate, Invest!

John-Paul explained that Hub Accra has “developed a three-phase impact model to help early stage entrepreneurs harvest their innovation and become investment-ready.” This model is known as, “Educate, Incubate, and Invest!”

Educate: OUWA is the primary partner in the education phase of the model. Located next to the hub, OUWA provides low-cost, online classes for Hub Accra’s members. A goal of the educational component of the model is to spark an interest in lifelong learning for the entrepreneurs, as well an awareness of various opportunities online for continuing education.

Incubate: Hub Accra has initiated an accelerator program for high-impact entrepreneurs with high growth potential – giving entrepreneurs daily structure and instruction on how to move forward with their ideas.

Hub Accra’s Collaborative Network

Invest: Once participants have graduated from either the incubator or accelerator programs, Hub Accra’s co-founding partner, SliceBiz, a micro-investment crowdfunding platform that provides seed funding, (I will introduce Slice Biz in more detail in my next blog post.) can gauge the investment readiness of their startups. Startups that show great potential with innovative business models will have the opportunity to raise seed funding through the SliceBiz platform.

Incubator Program

As stated in the three-phase model, students who complete the certificate in entrepreneurship have the opportunity to enter Hub Accra’s incubator program, “Startup West Africa.” John-Paul’s plan is to enroll approximately ten startups biannually in the program. He anticipates that the average entrepreneur will progress from the entrepreneurship program through the incubator/accelerator to investment in approximately 18 months.

Hub Accra’s 2nd Level Working Space for firms in the Accelerator Program.

The incubator program meets several times per week offering workshops, team-building exercises, business plan development assistance, and connections to industry professionals for mentorship. In return for the services provided, entrepreneurs are asked to reserve up to 5% equity in their company for Hub Accra or pay modest fees to contribute to the sustainability of the hub’s business model.

The Way Ahead

John-Paul is dedicated to expanding Hub Accra’s presence and deepening its impact in Ghana. Within the next few years he hopes to shift to a larger facility that is specifically built for their needs, to truly leverage the current momentum, and realize the potential of their model.

This new hub will feature fully developed educational and investment facilities as well as ample space for startups to grow. John-Paul anticipates offering office space to key partners to operate out of their Hub to nurture the community. He would also like to provide living space to house entrepreneurs, entrepreneurs-in-residence, and international guests.

His goal is to accommodate approximately 40 startups concurrently in this co-working space, spawning 100 sustainable businesses over a five-year period. He estimates that these startups will employ approximately 400+ people within the first five years of operation.

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Bitcoin and decentralized notary services for information sharing

#NetworkScience

Bitcoin, https://bitcoin.org/en/, is:

• an electronic payment system and also

• an electronic currency (albeit a very volatile currency).

Bitcoin has several properties, [cite ted series]:

• Privacy (users can conduct transactions using pseudonyms)

• Open (the underlying technology is open for anyone to use)

• Anyone can use it (as much as half of the world population does not have a traditional bank account, http://www.deloitte.com/assets/Dcom-UnitedStates/Local%20Assets/Documents/FSI/US_FSI_Bankingtheunbanked_043012.pdf )

• Distributed (no chargeback capability since bitcoin is used like cash)

Bitcoin depends upon use of cryptographic hash functions. Cryptographic hash functions are mathematical transformations which take a message and produce a “digest” or “tag” or “hash/fingerprint”. The message can be of arbitrary size but the digest will be of fixed length output (sha256, http://en.wikipedia.org/wiki/SHA-2 , has a 256 bit output). A cryptographic hash function has certain properties:

• Computationally efficient

• Collision resistant (it is hard to find two messages that have the same hash output)

• The hash output should hide information about the input message

• The output should look random

A remarkable result was achieved along the way to implementing the Bitcoin ecosystem. That result, the “bitcoin block chain” enables a network of individuals to agree on a given outcome in the presence of potentially malicious activities by members of the network to prevent agreement. Business Insider of Australia gave their Person of the Year award for 2013 to Satoshi Nakamoto, the pseudonymous creator of Bitcoin, http://www.businessinsider.com.au/the-future-of-the-blockchain-2014-4 . The reason that Satoshi Nakamoto received this award was because the bitcoin block chain result constitutes a solution to the “double spend” spend problem or the “Byzantine Generals” problem, http://research.microsoft.com/en-us/um/people/lamport/pubs/byz.pdf . It seems to me that the result may be able to be used to provide decentralized notary services for information sharing.

That is, the purpose of this short note is to assert that the “bitcoin block chain” approach to solving the Byzantine Generals problem may be modified/extended to establish a solution for decentralized notary services for information sharing. Recently Andreas Antonopouloulos asserted that there are now over 200 different bitcoin-based currencies available on the Internet and predicts many more to come since currencies are the cultural way of assigning value, https://www.youtube.com/watch?v=KLj2X8ml-CI . One service is available to create your own version of currency (if you want to spend about $10) using the open-source bitcoin solution, http://www.theguardian.com/technology/2014/jan/07/bitcoin-me-how-to-make-your-own-digital-currency.

Thus, an interesting student/faculty project would be to extend the recent “need to share” result, http://www.usma.edu/nsc/SiteAssets/SitePages/Publications/report1.pdf , to incorporate the “bitcoin block chain” result to create a decentralized approach for (1) valuing information to be shared, (2) providing a decentralized notary service for “trusting” assertions concerning the provenance, and integrity of the information to be shared, (3) sharing that information in real-time over a cloud architecture in which all participants have access to encrypted copies of all of the information, and (4) enabling any portions of the information to be shared with any of the individuals or groups in the information sharing ecosystem based upon appropriate assertions of a “need to share” information security policy by the “owner” of the (valued) information.

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Clan Dynamics in Somali Piracy Part II

#NetworkScience

Part I of this series discussed how the Networks of Somali Piracy dataset had created results parallel to that of the qualitative work of scholars working on the topic.  Specifically, the networks generated by the project had shown the clan dynamics within Somali piracy by revealing the almost complete separation of acts by clans during 2012. However, the effects of clan dynamics permeate far beyond the actual operations of pirates.  While the clan system of Somalia does not have definitive borders within the country, the region of Puntland (the Northeastern region of the country) which is home to most of the pirates is generally home to only two of the major clan families that have their own distinct territories (with the Hawiye being in the south of Puntland and the Darod being in the North).

As such, if clan dynamics are truly central to the practice of piracy, then this will also show up significantly within the regions where piracy is practiced and where ships are held awaiting ransom.  Again, our dataset from 2012 validated this, with each clan having its own distinct region where their prey are taken and held

Again, we can easily see that there is no crossover or major cooperation within the clans, leading to a complete separation even of territories within which piracy is practices. As such, even the location to which a captured ship has been taken can inform us as to which clan must be dealt with and eventually even the principal actors involved.  Again this strikes on the point that while much of the generalist work done on Somali piracy ignores the issue of clan dynamics, these are central to the understanding of the practice.  By simply ignoring these, as much of the literature unfortunately does, one ends up with an incomplete and often inaccurate view of Somali piracy as a monolithic construct as opposed to a nuanced practice with many actors in many locations, all of whom need to be engaged.

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Network Science Education for All Ages

#NetworkScience

The Network Science Center has been busy over the last month broadening awareness of network science as an interdisciplinary field of study. NSC researchers, Lori Sheetz, Luke Gerdes, and Jocelyn Bell, have taught Introduction to NS classes to students at the Youth Center here at West Point, to teachers up in Newburgh, and last week to middle school students from all over the United States as part of the Middle School STEM Workshop. When asked, ‘What is a network?’, many people immediately think of facebook or the internet, but few understand the interdisciplinary breadth of the field and its many applications. These classes allow NSC to share basic understanding and some fun applications so that the students begin to see and think about the networks they interact with every day.

A group of NSC researchers also had an opportunity to work on new initiatives, share research, and build collaborations at the NetSci 2014 conference in Berkeley, CA 1-6 June. Lori Sheetz participated in a ‘Network Science Literacy Working Group’ to outline basic network concepts every citizen should understand. Chris Arney, Kate Coronges, and Lori Sheetz were also all organizers and speakers at three separate satellite symposiums held before the main conference; Cooperative Team Networks, NetSciEd3: Satellite Symposium on Network Science in Education, and Network Science for National Defense. The main conference was a valuable time to hear about current research and meet with collaborators. Dan Evans attended the main conference and presented a poster at the Thursday night session.

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Clan Dynamics in Somali Piracy Part I

#NetworkScience

While the next phases of studies into networks of Somali armed groups is being prepared, the Central Node will be used to share some of the preliminary results of the study that has been carried out so far by myself and Cadet Eric Warren.  Following the information gathering that has been covered in a previous post, we began to compare the results of our dataset and the generated networks with the assessments that had been made in the more qualitative studies that exist.

Perhaps the first major issue involved is the absence of the ‘Somali’ in the Somali piracy.  While much of the qualitative work discusses the operational issues involved in piracy or specific acts of piracy, it often ignores the actual individuals engaged and the social dynamics that shape the practice of piracy.  This is rampant throughout the journalistic accounts and often finds its way to the more general studies.  Even those that make a token effort at mentioning the complex clan and sub-clan structure around which Somali society is organized rarely made use of that information to offer a more nuanced analysis of the piracy in the Gulf of Aden.  In the end, it was only the work of those scholars and writers that physically travelled to the locations of piracy and worked within the Somali population, such is Stig Jarle Hansen and Jay Bahadur, which managed to offer a central discussion of what made Somali piracy actually that of Somalis and not an undifferentiated practice.

The clan dynamics that authors like Hansen and Bahadur discuss permeate the practice of piracy and how it functions along the coast of Somalia.  Hansen specifically notes that the basic practice of piracy is built around clan groups and Bahadur concurs.  Our own data parallels this, as shown in the visualization below (prepared by Louis Boguchwal):

As can be seen, event a surface visual reading allows for the conclusion that clan dynamics are at play in the acts of pirate gangs.  There is only a single major cross-clan operation shown within the 2012 dataset and that ended with a significant falling out that saw a firefight between the Hawiye and Dir collaborators.  Aside from that, at least at the clan level, there is no crossover.  While this is not necessarily surprising to scholars of Somali society, its absence from most of the discussions of the issue of piracy off of Somalia has warped the discussions of solutions to the problem.

Part II will discuss how these clan dynamics translate to an understanding of territorial control and use of ports by various pirate groups.

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Newsblast Volume 4 Issue 7

#NetworkScience

In the current issue of the Network Science Center Newsblast Dan Evans and Louis Boguchwal discuss and evaluate different methods for comparing networks. This is critical in their research which seeks to compare entrepreneurial environments.  You can also find a link to a recent article on, ‘Power Grid Defense Against Malicious Cascading Failure’. To read their article in this issue of the Network Science Center’s Newsblast, click here.

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NetSel – Network Analysis for Participant Selection

#NetworkScience

Since 2003, the Army’s Capabilities Integration Center (ARCIC) has run a year-long series of studies, workshops, and wargames, known collectively as Unified Quest.  The focus of this program is to examine the Army’s future challenges, issues, and potential solutions.  The outcomes from the wargames help shape policy and budget for the Army.  For example in Unified Quest 2012: Building Partners and Partner Capacity, participants identified the need of the Army to develop regional expertise, cultural awareness, and language skills.A critical factor that drives wargame outcomes is the group of participants.  Therefore, we seek a solution to ensure the Army is gaining valuable information from the wargames.  To this end, we utilize network science and the technique of structural equivalence to select an optimal group of participants.  Our methods examine potential participants’ attributes, such as academic background, professional sector, military experience, and languages spoken.

Specifically, structural equivalence methods compare participants to benchmark “ideal individuals” for a particular wargame, called archetypes, defined by the stakeholder.  An archetype represents the stakeholders’ beliefs that an individual possessing this set of attributes in combination will be able to generate productive contributions to the wargame.  Each of the archetypes is designed to fill a certain role or niche within the wargame.  For example, in a wargame looking at biological warfare we would have an archetype named “Scientist,” who would likely possess the attributes chemistry, physics, and research.  The idea is that this single individual will more effectively contribute to the wargame by the synergistic effects of his or her constituent attributes.  This is preferable to three individuals who each possess one of these attributes because they are limited to drawing only on specific, targeted experiences when solving a problem, rather than a holistic perspective derived from multiple types of experiences.  An example of one potential participant and one “ideal participant” with their respective attributes is shown below.

We can see in the network visualization that Person 1 shares three attributes with Ideal 1: Research, Infantry, and Academia.  Person 1 shares three out of seven Archetype 1 attributes, yielding a score 3/7 = 42.9%.  This is the premise of our participant scoring and selection process.  The more attributes that a potential participant shares with the “ideal participant,” the more likely they are to be selected for the wargame.

In addition to individual scores, we also calculate a “group optimality score,” that quantifies the overall quality of the selected group.  This score is a simple average of selected participant scores.  Stakeholders can use group optimality score to gauge group improvement with the introduction of new participants.

Our team, CDT Zachary Langhans, Mr. Louis Boguchwal, Mr. Daniel Evans, CPT Nathaniel Bastian, and Dr. Jocelyn Bell, developed a methodology and an algorithm to score, rank, and ultimately select individuals for each archetype, and optimize the group overall.  The outcome of this project is an automated toolkit that will be utilized by ARCIC for their future wargames.  Example output is shown below.

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NetSci High students win scholarships

#NetworkScience

Congratulations to three students from last year’s NetSci High teams for receiving scholarships from the New York State Science Honor Society. Bhavana Patil and Lauren Cooke both received first place awards and Simonne Cazoe received a second place award.

For the last  two years the Network Science Center at West Point has mentored teams of high school students who are conducting yearlong network science research as part of NetSci High, a three year project funded by the National Science Foundation. Last year the two teams of students wrote and administered a survey and then created  communication networks of the students at both campuses of Newburgh Free Academy. One team used the dataset to research the communication between the two campuses and the second team studied differences between students’ face-to-face communication and electronic communication. The students learned much about networks, the research process, and collaboration with peers. At the end of the project the students’ research was presented in Copenhagen, Denmark at NetSci 2013, an international network science conference. The teams also presented their research in Boston last July.  Many of the students who participated in the research project remarked that this experience helped them to further develop their interest in STEM fields and learn skills that would help them succeed in college and also later in the work place.

Currently NSC is mentoring three teams as part of the second year of the program. One team is looking at the influence at the 1787 Constitutional Convention. A second team chose a digit humanities project and is using networks to analyze character interactions in contemporary fiction. The final team is analyzing reddit as a multilayer network. It is exciting to see how network science is beginning to be utilized in research at the undergraduate and now high school levels.

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Network Comparison Methods, an Evaluation

#NetworkScience

As detailed in a previous Network Science Center Newsblast, the goal of our research is to compare the entrepreneurial ecosystems in different locations. Mathematically, comparing entrepreneurial environments equates to comparing networks.  To what degree are two networks the same or different?  This illustration is a bit simplistic but gets to the general goal.

Are the following two networks similar or different, mathematically, and if they are different, how so?

Our team conducted an extensive literature review and to our surprise, we found that network comparison methods remain scarce.  Current methods are imprecise and lack technical rigor.  The list below summarizes the approaches that we have explored:

  • Simple Metrics
  • Structural Comparison and Fitting
  • Connectedness and Robustness
  • Future-Oriented Dynamic Analysis
  • Exponential Random Graph Models – our method of choice

Simple Metrics

We first consider simple metrics, such as node-level centrality metrics.  The network science community typically uses degree, betweenness centrality, closeness centrality, and eigenvector centrality to assess the importance of particular nodes.  To characterize a network as a whole using these metrics, we can either examine centralizations or directly analyze centrality distributions.  Centralization quantifies how influential the most important node in the network is relative to all others, and can be evaluated with respect to any centrality metric.  Alternatively, a researcher could analyze the distribution of a particular metric, which details the proportion of nodes in the graph with a specific centrality value.  Then, networks could be classified and compared based on their centralizations and centrality distributions.

However, these simple metrics these metrics are highly sensitive, and provide imprecise “high level” descriptions of networks.  Consequently, these measurements would not inform researchers into the inner workings of the systems they represent.  Small modifications to a network can radically change the aforementioned metrics:

  • Minor changes to the number of nodes or edges
  • “Rewiring” a small proportion of edges
  • Slight changes to edge weights

We also note that these modifications arise with errors in data collection, a problem all too familiar to the network science community.  It would be difficult to argue that simple metrics adequately compare networks when the metrics depend so heavily on reliable data.  Two networks could actually be similar with very different metrics, or quite different with similar metrics.

Structural Comparison and Fitting

Network scientists have already addressed the problems with simple metrics described above, with generally accepted structural characterizations.  Some popular structures found in the literature are star, circle, Erdős–Rényi, small-world, and scale-free networks.  Star networks contain edges only from a center node to all others, making them highly centralized.  In contrast, circle networks are highly decentralized, and contain edges between adjacent nodes, forming a ring.  Erdős–Rényi random networks arise when the existence of edges is subject to assigned probabilities.  Small-world networks are formed by randomly “rewiring” some edges of a nonrandom lattice structure.  This rewiring drastically reduces shortest path lengths between node-pairs throughout the network.  Scale-free networks exhibit a degree distribution obeying a power-law.  The proportion of nodes in the network with degree k obeys P(k) ~ k, where γ is a parameter typically between 2 and 3.  Researchers can formally classify other networks by specifying a particular degree distribution.  Networks in the same category could be deemed “similar.”  For network structures that are based upon degree-distributions we could use statistical tests, such as a Chi-squared test, to determine if the network in question fits the postulated distribution.

Connectedness and Robustness

While these structural frameworks improve upon the descriptive strength of simple metrics they are still inadequate.  Just because two networks can be classified into the same broad structural category does not mean they are similar.  Also, real-world networks do not fit neatly into predefined categories.  It is rare to find a network that can be perfectly described by one of these models.  Statistically-based distribution fitting also proves ineffective.  When performing a Chi-squared test we might reject the null hypothesis of a specified distribution for many, or all, networks under consideration.  This could happen because few networks are well-described by a particular distribution.  In this case, rejecting numerous hypotheses has not brought us any closer to understanding our observed networks, nor comparing them.

The concept of a network’s robustness against node or link deletions has long been a part of the network science literature.  Examples include node and edge connectivity.  These figures represent the minimum number of nodes or edges that must be removed to disconnect a graph.  Networks exhibiting similar robustness metrics could be said to be similar.

But observe, robustness measures themselves are sensitive to minor modifications in network structure, and carry the same burdens as their simple metric counterparts.  Also note that connectedness figures do not account for network size, in terms of node-set or edge-set cardinalities.  Two networks could have the same connectivity, yet differ in size.

Future-Oriented Dynamic Analysis

Many real-world networks represent dynamic processes, with ties changing over time.  Ties present now may absent later, and ties absent now may be present later.  We could observe networks at discrete time points and attempt to predict their future structures.  It might be informative to compare networks by their future structures.  This projection comparative approach could be complemented with classic forecasting techniques such as exponential smoothing.  Two networks could be declared similar if they are projected to have similar characteristics, such as counts of local structures (e.g., reciprocated ties) or summary statistics (e.g., mean degree).  Alternatively, network “transition paths” could be compared.  Networks could be deemed similar if the way they change over time is similar.

But how would we select an end-point?  Two networks might look similar at some future times, but not others.  It would be arbitrary to pick the time for which the projected state comparison should take place.  Further, comparisons based on projections are risky and would likely lead to invalid comparisons, even with troves of data.  However, comparing network evolution is safer than projection because it involves documenting observed changes in real data.  It is most meaningful to track changes in particular characteristics and local structures.  But to track these salient characteristics we must first identify them.  The current project is a prerequisite, and this temporal aspect constitutes a natural extension.

Exponential Random Graph Models

Exponential Random Graph Models (ERGMs), our method of choice, provide a statistical framework to analyze the forces governing link-formation in networks.  ERGMs adapt logistic regression techniques, where the dependent variable is binary, to account for dependencies inherent to networks.  One approach to comparing networks is to use the ERGM fit from one observed network to predict another observed network.  Then we could analyze the error.  Further, we could gauge the goodness-of-fit of one network’s ERGM with respect to another network.  Researchers have begun to explore these techniques.  But beyond the estimation of the ERGM itself, these methods are not statistically rigorous.  They are begging for extension, which is where this project picks up.

Our network comparison extension is as follows.  We aim to compare coefficients across models.  To compare two networks, we fit two ERGMs, one for each observed network.  This is analogous to estimating two logistic regression models, each with a different dependent variable and the same set of explanatory variables.  Then we will compare parameters associated with the same explanatory variable to determine if the effects are similar in each system, i.e., network.  Specifically, we seek to determine whether the parameters are statistically different from one another.  Parameter comparison would allow us to see if the same forces govern two networks, and if the forces have the same magnitude of effect.  Two networks are deemed similar if their ERGM parameters for the same explanatory variable are statistically similar, in terms of magnitude.  More “common-magnitude parameters” means greater similarity.  The merits of these comparative ERGM approaches, currently under development, are their statistical rigor without depending on imprecise global structural properties.

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