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BALANCE

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Testing Two Theories for Generating Networks

Multiple social processes generate social network structures. We use relaxed structural balance, a generalization of classic structuralbalance, to facilitate a direct comparative test of two social psychologicaltheories regarding network generation. One is structural balance theory. Theother concerns differential popularity. These theories predict distinctivesigned blockmodels. We use two well known empirical temporal signed datasets presenting an opportunity for comparing the two theories in terms oftheir predictions about blockmodel representations of these networks. Theresults provide strong support for differential popularity, differentialdisliking, and mutual disliking within a subset of actors. While there isevidence that structural balance was also operating, it seems the lesser processfor the data used in these tests. We also examine the unequal distributions ofreceiving positive and negative ties. Both tend to become more unequal overtime. Suggestions for future research are provided.

Partitioning Large Signed Two-mode Networks

While a substantial amount of attention within social network analysis (SNA) has been given to the study of one-mode networks, there is an increasing consideration of two-mode networks. Recent research on signed networks resulted in the relaxed structural balance (RSB) approach and its subsequent extension to signed two-mode networks involving social actors and social objects. We extend this approach to large signed two-mode networks, and address the methodological issues that arise. We develop tools to partition these types of networks and compare them with other approaches using a recently collected dataset of United Nations General Assembly roll call votes. Although our primary purpose is methodolog-ical, we take the first step towards bridging Heider’s structural balance theory with recent theorizing in international relations on soft balancing of power processes.

Partitioning Signed Two-mode Networks

Structural balance theory forms the foundation for a generalized block model method useful for delineating the structure of signed social one-mode networks for social actors (for example, people or nations). Heider’s unit formation relation was dropped. We re-examine structural balance by formulating Heider’s unit formation relations as signed two-mode data. Just as generalized block modeling has been extended to analyze two-mode unsigned data, we extend it to analyze signed two-mode network data and provide a formalization of the extension. The blockmodel structure for signed two-mode networks has positive and negative blocks, defined in terms of different partitions of rows and columns. These signed blocks can be located anywhere in the block model. We provide a motivating example and then use the new blockmodel type to delineate the voting patterns of the Supreme Court justices for all of their nonunanimous decisions for the 2006–07 term. Interpretations are presented together with a statement of further problems meriting attention for partitioning signed two-mode data.

Partitioning signed networks

Structural balance theory has proven useful for delineating the blockmodel structure of signed social networks. Even so, most of the observed signed networks are not perfectly balanced. One possibility for this is that in examining the dynamics underlying the generation of signed social networks, insufficient attention has been given to other processes and features of signed networks. These include: actors who have positive ties to pairs of actors linked by a negative relation or who belong to two mutually hostile subgroups; some actors that are viewed positively across the network despite the presence of negative ties and subsets of actors with negative ties towards each other. We suggest that instead viewing these situations as violations of structural balance, they can be seen as belonging to other relevant processes we call mediation, differential popularity and internal subgroup hostility. Formalizing these ideas leads to the relaxed structural balance blockmodel as a proper generalization of structural balance block models. Some formal properties concerning the relation between these two models are presented along with the properties of the fitting method proposed for the new blockmodel type. The new method is applied to four empirical data sets where improved fits with more nuanced interpretations are obtained

Two Algorithms for Relaxed Balance Partitioning

Understanding social phenomena with the help of mathematical models requires a coherent combination of theory, models, and data together with using valid data analytic methods. The study of social networks through the use of mathematical models is no exception. The intuitions of structural balance were formalized and led to a pair of remarkable theorems giving the nature of partition structures for balanced signed networks. Algorithms for partitioning signed networks, informed by these formal results, were developed and applied empirically. More recently, ‘‘structural balance’’ was generalized to ‘‘relaxed structural balance,’’ and a modified partitioning algorithm was proposed. Given the critical interplay of theory, models, and data, it is important that methods for the partitioning of signed networks in terms of relaxed structural balance model are appropriate. The authors consider two algorithms for establishing partitions of signed networks in terms of relaxed structural balance. One is an older heuristic relocation algorithm, and the other is a new exact solution procedure. The former can be used both inductively and deductively. When used deductively, this requires some prespecification incorporating substantive insights. The new branch-and-bound algorithm is used inductively and requires no prespecification of an image matrix in terms of ideal blocks. Both procedures are demonstrated using several examples from the literature, and their contributions are discussed. Together, the two algorithms provide a sound foundation for partitioning signed networks and yield optimal partitions. Issues of network size and density are considered in terms of their consequences for algorithm performance.

Networks in Social Psychology — Lewin

Historical accounts of academic disciplines are varied, incomplete, and often controversial. They are attempts to identify the intrinsic features of disciplines and so identify boundaries between them. As such, they are limited because disciplines are sprawling collections of ideas that spread over these boundaries and involve some people who actively stretch boundaries when pursuing research ideas. This essay goes beyond a simple historical account by tracing some older ideas to examine their contemporary relevance. Also, the work of Kurt Lewin (1890-1947) cannot be contained within a single discipline. Disciplines also change, sometimes dramatically, over time when new data are obtained, new methods are developed, new paradigms are adopted, and new theories are developed. Despite their differences, all historical accounts feature people and places as well as content. Lewin is one of the creators of group dynamics as a set of methods for studying human groups. He also played a role in the development of modern social network analysis. Forsythe (1990) provides a detailed treatment of group dynamics and Freeman (2004) presents a comprehensive account of the emergence of social network analysis, one that is focused on ideas. Rightly, both books consider contributions from Lewin.

Multiple Indicator Approach to Blockmodeling

Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, generalized blockmodeling faces a pair of vulnerabilities. One is sensitivity to poor quality of the relational data and the other is a risk of over fitting block models to the details of specific networks. Over fitting blockmodels can lead to multiple equally well fitting partitions where choices cannot be made between them on a principled basis. This paper presents a method of tackling these problems by viewing (when possible) observed social relations as multiple indicators of an underlying affect dimension. Quadratic assignment methods using matching coefficients, product moment correlations and Goodman and Kruskal’s gamma are used to assess the appropriateness of using the sum of observed relations as input for applying generalized blockmodeling. Data for four groups are used to show the value of this approach within which multiple equally well fitting blockmodels for single relations are replaced by unique (or near-unique) partitions of the summed data. This strategy is located also within a broader problem of blockmodeling three-dimensional networks data and suggestions are made for future work.

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BLOCKMODELING

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Two-mode KL Means Clustering

The two-mode KL-means partitioning (TMKLMP) problem has a number of important applications in thesocial and physical sciences. For example, the intra-block variability measure associated with TMKLMPunderscores its direct relevance to two-mode homogeneity blockmodeling of binary and real-valuedsocial networks. We present a real-coded genetic algorithm for obtaining TMKLMP solutions. A simulationstudy showed that the new algorithm compares favorably to a multistart implementation of a two-mode KL-means heuristic, which is recognized as a top-performing method for TMKLMP. The merit ofthe proposed method is demonstrated via an application to the blockmodeling of social network dataassociated with signing of environmental advertisements in the New York Times as a part of the TurningPoint Project.

Variable Neighborhood Blockmodeling

This paper presents a variable neighborhood search (VNS) algorithm that is specially designed for the blockmodeling of two-mode binary network matrices in accordance with structural equivalence. Computational results for 768 synthetic test networks revealed that the VNS heuristic outperformed a relocation heuristic (RH) and a tabu search (TS) method for the same problem. Next, the three heuristics were applied to two-mode network data pertaining to the votes of member countries on resolutions in the United Nations General Assembly. A comparative analysis revealed that the VNS heuristic often provided slightly better criterion function values than RH and TS, and that these small differences in criterion function values could sometimes be associated with substantial differences in the actual partitions obtained. Overall, the results suggest that the VNS heuristic is a promising approach for block modeling of two-mode binary networks. Recommendations for extensions to stochastic block modeling applications are provided.

An Exact Algorithm for Two-mode Blockmodeling

We consider problems where relationships between two sets (or modes) of objects are available in the form of a binary matrix with elements of 1 (0) indicating a bond (lack of a bond) between corresponding row and column objects. The goal is to establish a partition of the row objects and, simultaneously, a partition of the column objects to form blocks that consist of either exclusively 1s or exclusively 0s to the greatest extent possible. This two-mode blockmodeling problem arises in several scientific domains. In the social sciences, two-mode blockmodeling is particularly relevant for social network analysis, where the goal is to simultaneously partition a set of individuals and another set of objects (e.g., events they attended, organizations they are affiliated with, etc.). The inherent computational challenge of simultaneously constructing partitions for two distinct sets of objects has fostered a reliance on heuristics for two-mode blockmodeling. We offer an exact algorithm and demonstrate its efficacy in a simulation study. Two applications to real-world networks are also provided.

Multi-objective Blockmodeling

To date, most methods for direct blockmodeling of social network data have focused on the optimization of a single objective function. However, there are a variety of social network applications where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a block model based on a single network matrix and (2) simultaneous optimization of multiple criteria for fitting a block model based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm.

Absent Ties and Treatments for Blockmodeling

An absent tie is one for which we have no information regarding its nature. Absent ties for a network is a set of such ties. This lack of information can be present anywhere in network data and has the potential to compromise the results of all network analytic tools. To assess this impact, we used real networks and based simulations on them by introducing varying amounts of absent ties. They were treated with four treatments of absent ties. Blockmodeling, using structural equivalence, was applied to the known networks and then to every treated network. The results were compared. The amount of absent ties, their treatments, the block structure of a network, and the level of reciprocity all have an effect of the adequacy of the results of blockmodeling. Reconstruction combined with imputation based on modal values was the best overall treatment. However, treatments of absent ties can work for some networks but not others and we recommend treatments of absent ties based on the form of networks.

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POLICE ACADEMY

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From Here on Out We are All Blue — Race is a Police Academy

Motivated by the complicated history of race relations in policing, this article offers a social network analysis of the formation of relationships between recruits in a police academy. While the quantitative analysis is the core of this article, it is framed by an ethnographic description of how the interaction order within the academy functions as a mechanism for maintaining racism within police organizations. The academy’s social infrastructure was designed to generate encounters between recruits of various races. Recruits were divided into subgroups, which generally reflected the overall demographics of the cohort, so recruits of different races could get to know each other. While this academy had some success in forming ties between Black, Latino, and White recruits, it fell short of achieving the stated ideal of “ we’re all blue.”  Our results suggest that achieving this ideal lies in a distant future.

Race and Social Engineering in a Police Academy

This research examined an attempt to facilitate racial integration by populating squads (i.e., workgroups) in a police academy with mixes of recruits that reflected the racial demographics of the larger cohort. This was part of the social infrastructure of the academy. Additionally, a fixed seating arrangement was considered as a second element of academy infrastructure capable of impacting racial integration. We examined the consequences of these academy components over time with regard to race by combining ethnographic accounts with social network data collected throughout the academy and using a variety of network analytic tools. These consequences with regard to race were examined as a part of social network evolution. The academy’s social arrangements did accelerate the creation of social knowledge of recruits about each other and the formation of friendship ties both within and between races. However, our results point to clear limitations to such infrastructural engineering and have implications for both recruitment to police academies and dealing with race. They shed light also on processes of homophily and group composition over time and have implications for studying social networks.

Space and Contexts of Social Networks

Frequently, social networks are studied in their own right with analyses devoid of contextual details. Yet contextual features – both social and spatial – can have impacts on the networks formed within them. This idea is explored with five empirical networks representing different contexts and the use of distinct modeling strategies. These strategies include network visualizations, QAP regression, exponential random graph models, blockmodeling and a combination of blockmodels with exponential random graph models within a single framework. We start with two empirical examples of networks inside organizations. The familiar Bank Wiring Room data show that the social organization (social context) and spatial arrangement of the room help account for the social relations formed there. The second example comes from a police academy where two designed arrangements, one social and one spatial, powerfully determine the relational social structures formed by recruits. The next example is an inter-organizational network that emerged as part of a response to a natural disaster where features of the improvised context helped account for the relations that formed between organizations participating in the search and rescue mission. We then consider an anthropological example of signed relations among sub-tribes in the New Guinea highlands where the physical geography is fixed. This is followed by a trading network off the Dalmatian coast where geography and physical conditions matter. Through these examples, we show that context matters by shaping the structure of networks that form and that a variety of network analytic tools can be mobilized to reveal how networks are shaped, in part, by social and spatial contexts. Implications for studying social networks are suggested.

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SLOVENE SCIENCE

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Classifying Scientific Disciplines in Slovenia

We explore classifying scientific disciplines including their temporal features by focusing on their collaboration structures over time. Bibliometric data for Slovenian researchers registered at the Slovenian Research Agency were used. These data were obtained from the Slovenian National Current Research Information System. We applied a recently developed hierarchical clustering procedure for symbolic data to the coauthorship structure of scientific disciplines. To track temporal changes, we divided data for the period 1986–2010 into five 5-year time periods. The clusters of disciplines for the Slovene science system revealed 5 clusters of scientific disciplines that, in large measure, correspond with the official national classification of sciences. However, there were also some significant differences pointing to the need for a dynamic classification system of sciences to better characterize them. Implications stemming from these results, especially with regard to classifying scientific disciplines, understanding the collaborative structure of science, and research and development policies, are discussed.

On the Dynamics of Slovene Science

Coauthorship links actors at the micro-level of scientists. Through electronic databases we now have enough information to compare entire research disciplines over time. We compare the complete longitudinal coauthorship networks for four research disciplines (biotechnology,mathematics, physics and sociology) for 1986–2005.We examined complete bibliographies of all researchers registered at the national Slovene Research Agency. Known hypotheses were confirmed as were three new hypotheses. There were different coauthoring cultures. However, these cultures changed over time in Slovenia. The number of coauthored publications grew much faster than solo authored productions, especially after independence in 1991 and the integration of Slovenian science into broader EU systems. Trajectories of types of coauthorship differed across the disciplines. Using blockmodeling, we show how coauthorship structures change in all disciplines. The most frequent form was a core-periphery structure with multiple simple cores, a periphery and a semi-periphery. The next most frequent form had this structure but with bridging cores. Bridging cores consolidate the center of a discipline by giving it greater coherence. These consolidated structures appeared at different times in different disciplines, appearing earliest in physics and latest in biotechnology. In 2005, biotechnology had the most consolidated center followed by physics and sociology. All coauthorship networks expanded over time. By far, new recruits went into either the semi-periphery or the periphery in all fields. Two ‘lab’ fields, biotechnology and physics, have larger semi-peripheries than peripheries. The reverse holds for mathematics and sociology, two ‘office’ disciplines. Institutional affiliations and shared interests all impact the structure of collaboration in subtle ways.

On the Dynamics of Scientific Systems

Coauthorship links actors at the micro-level of scientists. Through electronic databases we now have enough information to compare entire research disciplines over time. We compare the complete longitudinal coauthorship networks for four research disciplines (biotechnology,mathematics, physics and sociology) for 1986–2005.We examined complete bibliographies of all researchers registered at the national Slovene Research Agency. Known hypotheses were confirmed as were three new hypotheses. There were different coauthoring cultures. However, these cultures changed over time in Slovenia. The number of coauthored publications grew much faster than solo authored productions, especially after independence in 1991 and the integration of Slovenian science into broader EU systems. Trajectories of types of coauthorship differed across the disciplines. Using blockmodeling, we show how coauthorship structures change in all disciplines. The most frequent form was a core-periphery structure with multiple simple cores, a periphery and a semi-periphery. The next most frequent form had this structure but with bridging cores. Bridging cores consolidate the center of a discipline by giving it greater coherence. These consolidated structures appeared at different times in different disciplines, appearing earliest in physics and latest in biotechnology. In 2005, biotechnology had the most consolidated center followed by physics and sociology. All coauthorship networks expanded over time. By far, new recruits went into either the semi-periphery or the periphery in all fields. Two ‘lab’ fields, biotechnology and physics, have larger semi-peripheries than peripheries. The reverse holds for mathematics and sociology, two ‘office’ disciplines. Institutional affiliations and shared interests all impact the structure of collaboration in subtle ways.

On the Dynamics of Scientific Systems — Reply

The comments of Everett (2011) and Light and Moody (2011) confirm our sense that, as apart of studying the dynamics of scientific change, we are tackling an interesting and important set of problems by using a wonderful data set.We appreciate their constructive critiques, especially their prompts to look more closely at the data we have. Their comments also make it clear that we are greatly indebted to the people at Institute of Information Science in Maribor (IZUM) for their maintenance of the Current Research Information System (SICRIS) and Cooperative Online Bibliometric and Services (COBISS) data archives. Without these data sets we could not study total disciplinary networks within the Slovene national science system.We are privileged in having access to these data.We agree with Everett (2011) about the value of comparing this national system with other such systems. However, we do not know of one and hope that our efforts could help promote the idea of creating comparable data sets in other nations. They may, indeed, exist and, if so, we would be more than willing to share ideas with researchers elsewhere regarding national scientific systems.

Collaboration in Scientific Communities

We combine two seemingly distinct perspectives regarding the modeling of network dynamics. One perspective is found in the work of physicists and mathematicians who formally introduced the small world model and the mechanism of preferential attachment. The other perspective is sociological and focuses on the process of cumulative advantage and considers the agency of individual actors in a network. We test hypotheses, based on work drawn from these perspectives, regarding the structure and dynamics of scientific collaboration networks. The data we use are for four scientific disciplines in the Slovene system of science. The results deal with the overall topology of these networks and specific processes that generate them. The two perspectives can be joined to mutual benefit. Within this combined approach, the presence of small-world structures was confirmed. However preferential attachment is far more complex than advocates of a single autonomous mechanism claim.

Dynamic Scientific Collaboration Networks

Network studies of science greatly advance our understanding of both the knowledge-creation process and the flow of knowledge in society. As noted in the introductory chapter, science can be defined fruitfully as a social network of scientists together with the cognitive network of knowledge items (Boerner et al, 2010). The cognitive structure of science consists of relationships between scientific ideas, and the social structure of science is mostly manifested as relationships between scientists. Here, we confine our attention to these relations. In particular, co-authorship networks among scientists are a particularly important part of the collaborative social structure of science. Modern science increasingly involves “collaborative research”, and this is integral to the social structure of science. Ziman argues that the organizational units of modern science are groups and not individuals (Ziman, 1994, pp. 227).1  Namely, co-authorship in science presents a more substantial indicator than just scientific communication in one way or another. In continuation, we focus on the dynamics of different kinds of co-authorship networks.