Decomposability and Relative Invariance: the Structural Approach to Network Complexity and Resilience

Abstract

AbstractEconomic complexity highlights the relationship between interdependence (a positional characteristic of elements belonging to a given network or structure) and connectivity (a functional characteristic of elements belonging to a given field of interaction). Positional interdependence (as the one between pieces in a jigsaw puzzle) is central to studies investigating the architecture of a complex system (Simon) while connectivity is central to the analysis of responsiveness patterns in social networks and strategic action fields. This paper discusses the fundamentals of a structural approach to economic and spatial complexity by highlighting the hierarchical arrangement of network elements as a distinctive feature of system identity. The positional distribution of network elements is a fundamental characteristic of complex networks and a central condition constraining the dynamics of those networks through the principle of relative structural invariance. The paper investigates the role of this principle by connecting it with the aggregation criterion followed in assigning network elements to specific subsystems. The type of aggregation is essential in determining the resilience properties of the network with respect to specific dynamic impulses. The paper concludes highlighting the need to combine the investigation of positional interdependence with the analysis of connectivity since positional interdependence is fundamental in determining which patterns of connection are more likely to arise (and which ones are excluded), due to the role of alternative properties of relative invariance constraining the feasible transformations in the positions of network elements.