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Authors:
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Maria Prosperina Vitale | University of Salerno | Italy

Giuseppe Giordano | University of Salerno

Giancarlo Ragozini | University of Naples Federico II | Italy

A multiplex network is a special case of a multilayer network that consists of a fixed set of nodes that interacts through different types of relationships. For this kind of data, the usual approaches consist of dealing with multiple relationships separately or of flattening the information embedded in all layers. This latter approach may lead to a loss of relevant information reducing the complexity of multiplex data. To cope with this issue, it could be useful to propose analytic tools that can be used to adapt multivariate methods to network data. In this regard, several factorial methods have been proposed in the social network analysis framework [3, 5), including attributes of nodes and events [4]. In the case of multiplex networks, canonical correlation analysis [2] was adopted to identify dimensions along which networks are related to each other, and an analytical procedure was recently introduced for dimension reduction using cluster analysis [7].

In this scenario, the present contribution aims at extending the use of factorial methods to visually explore the hidden structure of multiplex networks preserving the inherent complexity. More specifically, we focus on one-mode networks, analyzing the corresponding set of adjacency matrices using the DISTATIS technique [1], that is, an extension of the multidimensional scaling applied to a set of distance matrices derived on the same set of objects. This technique allows to represent the different kinds of relationships both in separate spaces and in a common space, called compromise. Therefore, it enhances the visual exploration of: i) the network structure in terms of nodes' similarity in each single layer, ii) the common structure of all layers, iii) the nodes' variation across layers, and iv) the similarity among the structure of layers.

In order to illustrate how the DISTATIS procedure works in practice for the treatment of multiplex networks, we consider a data set containing different kinds of relationships between 61 employees of the Computer Science Department at Aarhus University -AUCS data-[6]. The results of the illustrative example indicate the high explicative power of the method in capturing similarities among relationships.

References

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