Assessing Fundamental Power Differences in Exchange Networks: Iterative GPI

Networks have been discovered for which Network Exchange Theory (NET Markovsky, Willer and Patton 1988; Lovaglia, Skvoretz, Willer and Markovsky 1995) fails to provide tenable predictions. Here we elaborate NET to create a more general method. We show not only when and where exchange networks break into simpler substructures, but propose rules to decisively classify networks and substructures as strong, weak, or equal power. In doing so, we advance general heuristics for power development in exchange networks and demonstrate the promise of an approach using reciprocal comparison of general heuristics, formal theory, and computer simulation

Growing Scale-Free Networks with Tunable Clustering

We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks like the power-law degree distribution and the small average geodesic length, but with the high-clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter - the average number of triad formation trials per time step.Comment: Accepted for publication in Phys. Rev.

Examining whether and how instructional coordination occurs within introductory undergraduate STEM courses

Instructors’ interactions can foster knowledge sharing around teaching and the use of research-based instructional strategies (RBIS). Coordinated teaching presents an impetus for instructors’ interactions and creates opportunities for instructional improvement but also potentially limits an instructor’s autonomy. In this study, we sought to characterize the extent of coordination present in introductory undergraduate courses and to understand how departments and instructors implement and experience course coordination. We examined survey data from 3,641 chemistry, mathematics, and physics instructors at three institution types and conducted follow-up interviews with a subset of 24 survey respondents to determine what types of coordination existed, what factors led to coordination, how coordination constrained instruction, and how instructors maintained autonomy within coordinated contexts. We classified three approaches to coordination at both the overall course and course component levels: independent (i.e., not coordinated), collaborative (decisionmaking by instructor and others), controlled (decision-making by others, not instructor). Two course components, content coverage and textbooks, were highly coordinated. These curricular components were often decided through formal or informal committees, but these decisions were seldom revisited. This limited the ability for instructors to participate in the decision-making process, the level of interactions between instructors, and the pedagogical growth that could have occurred through these conversations. Decision-making around the other two course components, instructional methods and exams, was more likely to be independently determined by the instructors, who valued this autonomy. Participants in the study identified various ways in which collaborative coordination of courses can promote but also inhibit pedagogical growth. Our findings indicate that the benefits of collaborative course coordination can be realized when departments develop coordinated approaches that value each instructor’s autonomy, incorporate shared and ongoing decision-making, and facilitate collaborative interactions and knowledge sharing among instructors

Music notation: a new method for visualizing social interaction in animals and humans

BACKGROUND: Researchers have developed a variety of techniques for the visual presentation of quantitative data. These techniques can help to reveal trends and regularities that would be difficult to see if the data were left in raw form. Such techniques can be of great help in exploratory data analysis, making apparent the organization of data sets, developing new hypotheses, and in selecting effects to be tested by statistical analysis. Researchers studying social interaction in groups of animals and humans, however, have few tools to present their raw data visually, and it can be especially difficult to perceive patterns in these data. In this paper I introduce a new graphical method for the visual display of interaction records in human and animal groups, and I illustrate this method using data taken on chickens forming dominance hierarchies. RESULTS: This new method presents data in a way that can help researchers immediately to see patterns and connections in long, detailed records of interaction. I show a variety of ways in which this new technique can be used: (1) to explore trends in the formation of both group social structures and individual relationships; (2) to compare interaction records across groups of real animals and between real animals and computer-simulated animal interactions; (3) to search for and discover new types of small-scale interaction sequences; and (4) to examine how interaction patterns in larger groups might emerge from those in component subgroups. In addition, I discuss how this method can be modified and extended for visualizing a variety of different kinds of social interaction in both humans and animals. CONCLUSION: This method can help researchers develop new insights into the structure and organization of social interaction. Such insights can make it easier for researchers to explain behavioural processes, to select aspects of data for statistical analysis, to design further studies, and to formulate appropriate mathematical models and computer simulations

Examining whether and how instructional coordination occurs within introductory undergraduate STEM courses

Instructors’ interactions can foster knowledge sharing around teaching and the use of research-based instructional strategies (RBIS). Coordinated teaching presents an impetus for instructors’ interactions and creates opportunities for instructional improvement but also potentially limits an instructor’s autonomy. In this study, we sought to characterize the extent of coordination present in introductory undergraduate courses and to understand how departments and instructors implement and experience course coordination. We examined survey data from 3,641 chemistry, mathematics, and physics instructors at three institution types and conducted follow-up interviews with a subset of 24 survey respondents to determine what types of coordination existed, what factors led to coordination, how coordination constrained instruction, and how instructors maintained autonomy within coordinated contexts. We classified three approaches to coordination at both the overall course and course component levels: independent (i.e., not coordinated), collaborative (decision-making by instructor and others), controlled (decision-making by others, not instructor). Two course components, content coverage and textbooks, were highly coordinated. These curricular components were often decided through formal or informal committees, but these decisions were seldom revisited. This limited the ability for instructors to participate in the decision-making process, the level of interactions between instructors, and the pedagogical growth that could have occurred through these conversations. Decision-making around the other two course components, instructional methods and exams, was more likely to be independently determined by the instructors, who valued this autonomy. Participants in the study identified various ways in which collaborative coordination of courses can promote but also inhibit pedagogical growth. Our findings indicate that the benefits of collaborative course coordination can be realized when departments develop coordinated approaches that value each instructor’s autonomy, incorporate shared and ongoing decision-making, and facilitate collaborative interactions and knowledge sharing among instructors

Fast Computing Betweenness Centrality with Virtual Nodes on Large Sparse Networks

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses time and space for weighted networks, where and are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in time for integer-weighted networks, where is the average weight of edges and is the average degree in the network. Considerable time can be saved with the proposed algorithm when , indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis

Group differences in reciprocity, multiplexity and exchange: Measures and application

Local forces structure social networks. One major and widely researched local force is reciprocity, often assumed to work homogeneously across actors-i. e., all actors are equally subject to the same level of force towards reciprocity. Other local forces, like multiplexity and exchange, are also often assumed to apply equally to different actors. But social theory provides us with ample arguments why such forces might be stronger in some subsets of actors than others, or why such forces might affect intergroup ties more than intragroup ties. In this paper we introduce standard measures to capture these group specific forces towards reciprocity, multiplexity, and exchange. All the measures control for differential tendencies of actors to initiate ties of various types. We also introduce a procedure by which differences in the strength of these forces between groups and subgroups can be statistically evaluated. © 2011 Springer Science+Business Media B.V

Reciprocity, multiplexity, and exchange: Measures

We introduce measures and statistical tests for multiplexity and exchange that are modeled on similar ideas developed for reciprocity quite early in the history of social network research. As properties of a multi-relation network, multiplexity, and exchange have almost as ancient a history as reciprocity, but have not been as intensively investigated from a methodological perspective. Multiplexity refers to the extent to which two ties, for example, advice and friendship, coincide over population; that is, do respondents name the same people as friends as the persons they nominate as individuals from who they seek advice. Exchange refers to the extent to which a tie of one type directed from person i to person j is returned by a tie of another type from j to i. We conceive of the current paper as the first part of a two-part paper, wherein the second part explores specific theoretical models for multiplexity and exchange. © Springer Science + Business Media B.V. 2007