A precise definition for complex systems has not been provided, but the study of systems with a large number of components whose interaction results cannot be easily predicted provides researchers with the possibility to classify some systems as complex systems by defining some common characteristics. The characteristics of complex systems can be discussed from two structural and functional perspectives. In this research, we will examine one of the most frequently observed structural patterns in real systems called nestedness. Nestedness is a special form of hierarchical structures in which the neighborhood of nodes with lower degree is covered by the neighborhood of nodes with higher degree. This concept was first used in the field of ecology studies and gradually made its way to other fields such as economics, business, artificial intelligence and the World Wide Web, and then it was quantified by four main criteria. Using the method of overlapping nesting of the export networks of the countries belonging to the European unio‎n, the Middle East and South America from 2008 to 2018, we examined them in two weighted and binary ways and we found that the nestedness of the weighted network is due to the simultaneous examination and comparison of the two characteristics of node degree and weight. The edges are less than the nestedness calculated for the similar binary network. In the next stage, we tried to increase the nestedness of the network by applying a threshold and homogenizing the distribution of the order degrees of the network. We also showed that the nesting of these three networks is constant regardless of the shape and size of the network, the average weight, edge density, and the average output degree of each node over time, and the increase or decrease of these features will not affect the nesting process.

كيوان آقابابائي ساماني

فرهاد شهبازي

فرهاد فضيله، اسماعيل عبدالحسيني سارسري