Rick Grannis

In recent years, models proposed by mathematicians and statistical physicists have modeled large-scale social networks, however, they have incompletely accounted for properties known to affect the patterning of individuals' relations with others. Furthermore, given that these ...

While a great many useful statistical models and visualizations have been developed to explore large-scale complex networks, fewer have attempted to relate these models to data generated by samples. While, in many fields, complete (or near-complete) data is widely available, and while the Internet has made even more readily available, complete data about large-scale complex networks sufficient to answer many compelling social science questions does not exist and cannot be reasonably generated. In these cases, sampling theory must be used to connect data to models. This proves difficult for a variety of reasons such as: data collection methodologies which, while attempting to overcome non-response bias, deviate from standard sampling practices; and, the non-independence of both first neighbors and second neighbors. This entry reviews some of the different ways which have been created to faithfully translate data sampled from large-scale complex networks into useful statistics.

The concept that we live in small world networks connected by short paths has proved fascinating. These networks, however, do not typically emerge as linear responses to individual-level changes; rather, subtle changes in relations produce extraordinarily different macrolevel outcomes. Similarly, nuances in how we conceptualize, define, and measure relations can lead to widely different network characterizations. I demonstrate this variability using a spectrum of interaction types and argue that the dependence of results on subtleties in definition or measurement makes theoretical interpretation difficult. I offer an index to calculate how much inaccuracy or imprecision relational definitions or data-gathering techniques can tolerate before results yield utterly different interpretations.

In a groundbreaking article, Moody and White (2003) introduced the concept of structural cohesion, simultaneously characterizing emergent communities and their internally embedded layers by the number of node-independent paths interconnecting individuals. Like many studies, however, they “corrected” the directionality discovered in some of their data. While often done for important purposes, doing so potentially confounds structural cohesion with unrelated concepts. Some relations, especially those relating to the dynamic aspects of social life, are inherently directed, in whole or in part, and it may prove worthwhile to respect this directionality. In this article, I recast structural cohesion in terms of directed social relations and identify four distinct ways of measuring it. In two example data sets—hiring relations among graduate programs and trust relations among neighborhood residents—I show that only strong embeddedness, a type of structural cohesion emerging from directed relations, proves to be a powerful, robust, independent explanatory factor. I further show that if the directionality in the data in these examples had been “corrected,” the importance of structural cohesion would have been dramatically undervalued.

Neighborhoods shape a variety of outcomes for children,  families,  and  residents  in  general, influencing behavior,  attitudes,  and  values  as well. While some neighborhoods foster continuous patterns of criminal activity, others develop  collective efficacy, the shared understanding that their  constituent  members  have  social  capital resources which they are mutually able and willing to use to achieve collective outcomes. Neighborhoods  cluster  outcomes,  some  of  which  cannot be accounted for in terms of the characteristics of the  individuals or households currently residing in them; they prove to be real communities with  enduring characteristic  patterns that survive the replacement of their constituent  members.  A  useful  neighborhood definition would be one that  helped us better understand  these  neighborhood  communities and    their    effects.    These    neighborhood
communities are not only geographically meaningful but geographically identifiable as well because the networks of interactions among neighboring  residents  which  produce  them,  which translate neighboring interactions into neighborhood communities and their effects, are constrained by predictable urban geographic substrates. New research has proposed behaviorally oriented definitions of neighborhoods,
defining them in terms of their potential for interaction among residents. Defining neighborhoods in this way provides a lens to focus more closely on neighborhoods as effect-generating communities emerging  from  the  networked  interactions  of  their constituent residents.

While a great many useful statistical models and  visualizations have been developed to  explore  large-scale  complex  networks,  fewer  have attempted to relate these models to data generated by  samples.  While,  in  many  fields, complete (or  near-complete)  data  is  widely  available, and  while  the  Internet  has  made  even  more readily available, complete data about large-scale  complex  networks  sufficient to  answer  many  compelling  social  science  questions  does  not  exist and cannot be reasonably generated. In these  cases, sampling theory must be used to connect  data to models. This proves difficult for a variety  of reasons such as: data collection methodologies which,  while  attempting  to  overcome  non-response bias, deviate from standard sampling  practices;  and,  the  non-independence of  both  first neighbors and second neighbors. This entry  reviews some of the different ways which have  been created to faithfully translate data sampled  from large-scale complex networks into useful  statistics.

In recent years, models proposed by mathematicians and statistical physicists have modeled large-scale social networks, however, they have incompletely accounted for properties known to affect the patterning of individuals’ relations with others. Furthermore, given that these models were limited to social milieu where complete data sets were available, a need remains to connect properties of these large-scale social networks with sampling theory. Using information typically
available in network surveys of individuals, I show that one can calculate the expected value of several important global network properties while simultaneously accounting for such known biases as transitivity or clustering. I then calculate how sampling errors propagate through these global formulas and show that these propagated errors are sufficiently small to allow one to reasonably estimate these global properties even with small samples. I successfully demonstrate this model
with three different types of large-scale social networks.

ISDM (Integrated Social Network Decision Models) is a methodology and tool kit which supports full planning cycles for SSTR, disaster relief and humanitarian missions in cross-cultural environments.  ISDM guides users in developing a decision model that enhances the efficient collection and analysis of model-related data, especially from non-cooperative populations. ISDM also guides users in useful analysis while seamlessly accounting for missing or incomplete data; finally reintegrating the findings into the decision model for understanding.
As part of our continued testing of ISDM, we conducted a one-day “flash” study at UCLA to verify that the entire system could function both rapidly and effectively as a single integrated unit.  The study involved one graduate student and several undergraduate students, none of whom had any prior exposure to the ISDM methodology or toolkit.  We presented them with a scenario in which an academic institution was greatly concerned about the pervasiveness of cheating on tests.  The scenario required the student team to address the problem of potential strategies, resources and inherent uncertainties by gathering data from students on campus.
The “flash” study dramatically demonstrated how rapidly ISDM could be used by untrained users as a complete process that begins with an uncertainty to be understood and ends with a confident decision based on robust analysis of empirical data.  The entire process for our “flash” study was completed in a fraction of a day!  The process steps comprised: (1) problem understanding; (2) survey generation; (3) data collection; (4) analysis; and (5) selecting an optimal strategy based on the new intelligence and enhanced understanding of the situation.

The large and growing interest in social network analysis has fueled an increased demand from the research and intelligence communities for social network data.  But while massive amounts of data are collected by military, government and commercial entities, very little of this data is available for research and analysis, due primarily to privacy concerns.  A highly promising approach to breaking this bottleneck is to synthetically generate massive amounts of high fidelity dynamic social network data with characteristics that closely reflect real world data, and to make the means of generation as well as the data available to research and analysts.  But there are significant technical challenges involved with the synthetic generation and application of social network data. 
I review an integrated, step-by-step approach to creating and applying realistic and useful synthetic social network data. We generate synthetic data by first pulling apart a real dataset in order to understand it at a comprehensive level. We then put it back together using a number of unique algorithmic methods, synthesizing data that is faithful to a broad array of characteristics of the individual interactions and the contexts that generated them.  We validate that our synthetic data does indeed correspond to the original data, not only in its latent characteristics but also in its manifest ones.  Each of these tasks – analysis, synthesis and validation -- is designed ensure that the end product is trustworthy and robust against artifacts potentially inherent in any single method.

Neighborhood communities are social entities and the geographic equivalents we use to measure them must focus on the social reality not just the physical one.  In introducing t-communities, Grannis (1998, 2005) theorized, but did not demonstrate, that residential street networks accurately map the neighbor networks which inter-relate the geographic and social aspects of neighborhoods.  I explore this process using three different community surveys, each of which independently illuminates a different aspect of neighbor networks.  I show that neighbor networks geographically coincide with t-communities more so than with neighborhood equivalents defined only by their boundaries, proving them to be more effective proxies for neighbor networks.  I found that, typically, residents of a t-community were three steps, or three degrees of separation, apart, neighbors of neighbors of neighbors.  Furthermore, most of the “community” in a t-community is a community of households with children.  Using t-communities as a neighborhood equivalent refocuses research on the relational aspect of neighboring.