Abstract
In this paper we develop a data-driven hierarchical clustering methodology to group the economic sectors of a country in order to highlight strongly coupled groups that are weakly coupled with other groups. Specifically, we consider an input-output representation of the coupling among the sectors and we interpret the relation among sectors as a directed graph; then we recursively apply the spectral clustering methodology over the graph, without a priori information on the number of groups that have to be obtained. In order to do this, we resort to the eigengap criterion, where a suitable number of groups is selected automatically based on the intensity and structure of the coupling among the sectors. We validate the proposed methodology considering a case study for Italy, inspecting how the coupling among clusters and sectors changes from the year 1995 to 2011, showing that in the years the Italian structure underwent deep changes, becoming more and more interdependent, i.e., a large part of the economy has become tightly coupled.
Highlights
The European Physical Journal Special Topics allows to identify the connections among such groups, which can be regarded as the “weak element of the chain”; such connections are often neglected or shaded by the high degree of coupling of some of the elements.The analysis of strongly coupled clusters can be used to complement key sector analyses [1,3], allowing to identify key clusters.In this paper, based on the preliminary results in [7], we present a data-driven hierarchical clustering approach to identify groups of tightly interdependent critical infrastructures or economic sectors, taking into account the intensity of the coupling among them
The outline of the paper is as follows: after some preliminary definitions, that conclude this introduction, we review the input-output economic model in Sect. 2; we review in Sect. 3 the spectral clustering methodology, and we present in Sect. 4 the proposed data-driven hierarchical clustering methodology
We develop a data-driven hierarchical clustering methodology that does not rely on a priori knowledge about the number of groups; instead, it is based on the eigengap criterion discussed in the previous section
Summary
The European Physical Journal Special Topics allows to identify the connections among such groups, which can be regarded as the “weak element of the chain”; such connections are often neglected or shaded by the high degree of coupling of some of the elements. We consider an input-output representation, where the relations existing in a set of interdependent sectors (infrastructures) is characterized in terms of the economic amount of commodities/services produced by one sector, which is required for the production of commodities/services by another sector (in the case of infrastructures, instead, the relation is expressed in terms of how much the severity of a failure affecting one infrastructure is transferred to the others).
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