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Cluster analysis of multiplex networks: Defining composite network measures
Institution:1. ETH Zürich, Chair of Social Networks, Clausiusstrasse 50, 8092 Zürich, Switzerland;2. University of Oxford, Nuffield College, New Road, Oxford OX1 1NF, United Kingdom;3. University of Groningen, Department of Sociology, Grote Rozentstraat 31, Groningen 9712 TG, The Netherlands;4. MTA-TK “Lendület” Research Center for Educational and Network Studies, [Hungarian Academy of Sciences], Országház utca 30, Budapest 1014, Hungary;1. Institute of Sociology, Academia Sinica, Taiwan, ROC;2. Department of Sociology, Beijing University, China;1. Stanford University, Department of Sociology, 450 Serra Mall, Building 120, Room 160, Stanford, CA 94305, United States;2. Stanford University, Computer Science Department, 353 Serra Mall, Stanford, CA 94305, United States;1. Department of Management and Marketing, North Dakota State University, Fargo, ND, 58102, United States;2. Department of Management, University of Kentucky, United States;3. Olin Business School, Washington University in St. Louis, United States;1. Faculty of Computer Science and Engineering, “Ss Cyril and Methodius University”, Skopje, Macedonia;2. Macedonian Academy of Sciences and Arts, Skopje, Macedonia;3. IKT-Labs, Skopje, Macedonia;1. University of Manchester, United Kingdom;2. University of Kentucky, United States
Abstract:Social relations are multiplex by nature: actors in a group are tied together by various types of relationships. To understand and explain group processes it is, therefore, important to study multiple social networks simultaneously in a given group. However, with multiplexity the complexity of data also increases. Although some multivariate network methods (e.g. Exponential Random Graph Models, Stochastic Actor-oriented Models) allow to jointly analyze multiple networks, modeling becomes complicated when it focuses on more than a few (2–4) network dimensions. In such cases, dimension reduction methods are called for to obtain a manageable set of variables. Drawing on existing statistical methods and measures, we propose a procedure to reduce the dimensions of multiplex network data measured in multiple groups. We achieve this by clustering the networks using their pairwise similarities, and constructing composite network measures as combinations of the networks in each resulting cluster. The procedure is demonstrated on a dataset of 21 interpersonal network dimensions in 18 Hungarian high-school classrooms. The results indicate that the network items organize into three well-interpretable clusters: positive, negative, and social role attributions. We show that the composite networks defined on these three relationship groups overlap but do not fully coincide with the network measures most often used in adolescent research, such as friendship and dislike.
Keywords:Multiplex networks  Multilayer networks  Dimension reduction  Cluster analysis  Peer perceptions  Adolescents
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