A partitioning approach to structural balance |
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| Institution: | 1. Department of Sociology, University of Pittsburgh, Pittsburgh, PA 15260, USA;2. Faculty of Social Sciences, University of Ljubljana 61109 Ljubljana, Slovenia;1. Section of Epidemiology, Department of Veterinary Public Health, Faculty of Veterinary Medicine, Kasetsart University, Thailand;2. Centre for Development Oriented Research in Agriculture and Livelihood Systems (CENTDOR), Cambodia;3. Emergency Centre for Transboundary Animal Diseases (ECTAD), FAO Regional Office for Asia and the Pacific (FAO-RAP), Thailand;1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense DK-5230, Denmark;2. Projet Coati, I3S (CNRS, UNSA) and INRIA, Sophia Antipolis, France;1. Departament de Física Fonamental, Universitat de Barcelona, Martí i Franques 1, 08028 Barcelona, Spain;2. Department of Mathematics, City University London, Northampton Square, London EC1V 0HB, UK;3. Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain;1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Xidian University, Xi’an, Shaanxi Province 710071, China;2. Center for Administration and Complexity Science, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, China;1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;2. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia |
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| Abstract: | The classic formulation of structural balance by Cartwright and Harary (Psychological Review, 63, 1956, 277–293) had the basic structural theorem that a balanced structure could be partitioned into two mutually antagonistic subgroups each having internal solidarity. Davis (Human Relations, 20, 1967, 181–187) extended this theorem for cases where there can be more than two such mutually antagonistic subgroups. We use these theorems to construct a criterion function for a local optimization partitioning procedure for signed digraphs. For any signed digraph, this procedure yields those partitions with the smallest number of errors, a measure of the imbalance in the graph, and an identification of those links inconsistent with both generalized and structural balance. These methods are applied to some artificial data and to the affect data from Sampson (A novitiate in a period of change: An experimental and case study of social relationships, Dissertation, Cornell University, 1968). The latter provides a positive test of a basic tenet of balance theory, that there is a tendency towards balance with signed relations in human groups. While these methods can be applied to all signed digraphs and signed graphs, the balance hypothesis is relevant only for affect ties. |
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