Abstract
A popular objective criterion for partitioning a set of actors into core and periphery subsets is the maximization of the correlation between an ideal and observed structure associated with intra-core and intra-periphery ties. The resulting optimization problem has commonly been tackled using heuristic procedures such as relocation algorithms, genetic algorithms, and simulated annealing. In this paper, we present a computationally efficient simulated annealing algorithm for maximum correlation core/periphery partitioning of binary networks. The algorithm is evaluated using simulated networks consisting of up to 2000 actors and spanning a variety of densities for the intra-core, intra-periphery, and inter-core-periphery components of the network. Core/periphery analyses of problem solving, trust, and information sharing networks for the frontline employees and managers of a consumer packaged goods manufacturer are provided to illustrate the use of the model.
Highlights
The problem of partitioning a set of actors into two clusters, core and periphery, is a well-studied problem in the social network literature [1,2,3,4,5,6,7,8]
First we present a formal statement of the maximum correlation core/periphery partitioning problem originally proposed in [1] and studied in [2]
The section presents the formal statement of the maximum correlation core/periphery partitioning problem that is studied in this paper
Summary
The problem of partitioning a set of actors into two clusters, core and periphery, is a well-studied problem in the social network literature [1,2,3,4,5,6,7,8]. We present the formal statement of the maximum correlation core/periphery partitioning problem that is studied in this paper This is followed by a description of the proposed simulated annealing heuristic. The correlation between the two binary vectors x and y can be computed efficiently using the constants defined above This is important because it allows for rapid recomputation of rXY(π) using simple updates to these constants each time the partition is modified by moving an actor from the core to the periphery or vice versa. Because h is removed from the periphery, it is necessary to decrease the intra-periphery violations (ones in the periphery submatrix) in accordance with h’s ties to other actors in the periphery This is accomplished as follows: vPðp0Þ 1⁄4 vPðpÞ À ðahj þ ajhÞ: fj1⁄46 hg2T0
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