Review of:Caldarelli, Guido and Catanzaro, Michele (2012) Networks: A Very Short Introduction (Ve... more Review of:Caldarelli, Guido and Catanzaro, Michele (2012) Networks: A Very Short Introduction (Very Short Introductions). Oxford University Press: Oxford
The Journal of Mathematical Sociology (JMS) published a special issue on Evolution of Social Netw... more The Journal of Mathematical Sociology (JMS) published a special issue on Evolution of Social Networks in 1996 under the responsibility of the two present guest editors. Gordon and Breach published in 1997 a volume that contained the original articles of the special issue together with three new articles (Doreian and Stokman, editors. Evolution of Social Networks, New York: Gordon and Breach, 1997). In the first JMS special issue and subsequent volume, a distinction was made between network dynamics and network evolution. We were primarily interested in studies that concentrated on the underlying mechanisms that induce network change. In other words, we were interested in network evolution and not only with network change. Partly as a consequence of this emphasis, most contributions in the first volume focussed on theory, methods, and simulation. In this respect, the first volume did not bridge the gap between theory and empirical testing. This induced our desire to edit a second volume on Evolution of Social Networks where modeling and empirical analyses are integrated or at least combined. The present special issue contains four of such contributions. A number of others will follow next year in the third special issue on the topic of Evolution of Social Networks.
One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller compr... more One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. Batagelj, Doreian, and Ferligoj developed a generalized approach to blockmodeling and methods where a set of observed relations are fitted to a pre-specified blockmodel. In the paper this generalized blockmodeling approach as implemented in program Pajek is described. An overview of the blockmodeling procedures in Pajek is given and is illustrated by some examples.
The goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller compr... more The goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. In the paper we present some basic ideas and developments in this area. 1 Basic Notions 1.1 Network Let E = {X 1 , X 2 , . . . , X n } be a finite set of units or units. The units are related by binary relations R t # E E, t = 1, . . . , r, r # 1 which determine a network N = (E, R 1 , R 2 , . . . , R r ) In the following we restrict our discussion to a single relation R described by a corresponding binary matrix R = [r ij ] nn where r ij = # 1 X i RX j 0 otherwise In some applications r ij can be a nonnegative real number expressing the strength of the relation R between units X i and X j . 1.1.1 Example: Student Government In Table 1 and Figure 1 the Student Government network is presented. It consists of communication interactions among twelve members and advisors of the Student Government at the Universit...
ABSTRACT Due to the limited amount of information contained in a graph when the abstracted relati... more ABSTRACT Due to the limited amount of information contained in a graph when the abstracted relations are represented in all or nothing terms, the Harary and Ross algorithm is unable to detect structural variation within cliques. By considering valued graphs it is possible to apply the algorithm to successive levels in the graph and hence detect cliques within cliques. Attention is also directed towards determining lines which, through their absence, mean that a set of points do not form a clique. As successive levels are considered both the lines that drop out and the cliques that remain are important.
This paper presents a variable neighborhood search (VNS) algorithm that is specially designed for... more 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 blockmodeling of two-mode binary networks. Recommendations for extensions to stochastic blockmo...
Review of:Caldarelli, Guido and Catanzaro, Michele (2012) Networks: A Very Short Introduction (Ve... more Review of:Caldarelli, Guido and Catanzaro, Michele (2012) Networks: A Very Short Introduction (Very Short Introductions). Oxford University Press: Oxford
The Journal of Mathematical Sociology (JMS) published a special issue on Evolution of Social Netw... more The Journal of Mathematical Sociology (JMS) published a special issue on Evolution of Social Networks in 1996 under the responsibility of the two present guest editors. Gordon and Breach published in 1997 a volume that contained the original articles of the special issue together with three new articles (Doreian and Stokman, editors. Evolution of Social Networks, New York: Gordon and Breach, 1997). In the first JMS special issue and subsequent volume, a distinction was made between network dynamics and network evolution. We were primarily interested in studies that concentrated on the underlying mechanisms that induce network change. In other words, we were interested in network evolution and not only with network change. Partly as a consequence of this emphasis, most contributions in the first volume focussed on theory, methods, and simulation. In this respect, the first volume did not bridge the gap between theory and empirical testing. This induced our desire to edit a second volume on Evolution of Social Networks where modeling and empirical analyses are integrated or at least combined. The present special issue contains four of such contributions. A number of others will follow next year in the third special issue on the topic of Evolution of Social Networks.
One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller compr... more One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. Batagelj, Doreian, and Ferligoj developed a generalized approach to blockmodeling and methods where a set of observed relations are fitted to a pre-specified blockmodel. In the paper this generalized blockmodeling approach as implemented in program Pajek is described. An overview of the blockmodeling procedures in Pajek is given and is illustrated by some examples.
The goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller compr... more The goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. In the paper we present some basic ideas and developments in this area. 1 Basic Notions 1.1 Network Let E = {X 1 , X 2 , . . . , X n } be a finite set of units or units. The units are related by binary relations R t # E E, t = 1, . . . , r, r # 1 which determine a network N = (E, R 1 , R 2 , . . . , R r ) In the following we restrict our discussion to a single relation R described by a corresponding binary matrix R = [r ij ] nn where r ij = # 1 X i RX j 0 otherwise In some applications r ij can be a nonnegative real number expressing the strength of the relation R between units X i and X j . 1.1.1 Example: Student Government In Table 1 and Figure 1 the Student Government network is presented. It consists of communication interactions among twelve members and advisors of the Student Government at the Universit...
ABSTRACT Due to the limited amount of information contained in a graph when the abstracted relati... more ABSTRACT Due to the limited amount of information contained in a graph when the abstracted relations are represented in all or nothing terms, the Harary and Ross algorithm is unable to detect structural variation within cliques. By considering valued graphs it is possible to apply the algorithm to successive levels in the graph and hence detect cliques within cliques. Attention is also directed towards determining lines which, through their absence, mean that a set of points do not form a clique. As successive levels are considered both the lines that drop out and the cliques that remain are important.
This paper presents a variable neighborhood search (VNS) algorithm that is specially designed for... more 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 blockmodeling of two-mode binary networks. Recommendations for extensions to stochastic blockmo...
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