Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

The Use of a Game Theory Model to Explore the Emergence of Core/Periphery Structure in Networks and Its Symmetry

In network systems characterized by complex interactions of various types, core-periphery structures can be found. In this paper, we deal with such questions as what processes can lead to the emergence of core-periphery formation, whether this structure is symmetric, and to what extent. Namely, the question of symmetry in a complex network is still the subject of intense research interest. Symmetry can relate to network topology, network relationships, and other processes on networks. To answer these questions, we modified the model of the classic social dilemma called the repeated prisoner’s dilemma (or repeated PD game) by adding the cost of maintaining relationships between the pairs of players (partners) and especially by adding the possibility of ending some relationships. We present the results of simulations that suggest that the players’ network strategy (i.e., partner selection or termination of relationships with some partners) is the driving force behind the emergence of a core-periphery structure in networks rather than the player’s strategy in PD. Our results also suggest that the formed core is symmetric, and this symmetry is a result of the symmetric interactions of core players. Our outcomes can help understand various economic or social questions related to creating centers or peripheries, including their symmetry in different network systems.

A Novel Information Theoretical Criterion for Climate Network Construction

This paper presents a novel methodology for Climate Network (CN) construction based on the Kullback-Leibler divergence (KLD) among Membership Probability (MP) distributions, obtained from the Second Order Data-Coupled Clustering (SODCC) algorithm. The proposed method is able to obtain CNs with emergent behaviour adapted to the variables being analyzed, and with a low number of spurious or missing links. We evaluate the proposed method in a problem of CN construction to assess differences in wind speed prediction at different wind farms in Spain. The considered problem presents strong local and mesoscale relationships, but low synoptic scale relationships, which have a direct influence in the CN obtained. We carry out a comparison of the proposed approach with a classical correlation-based CN construction method. We show that the proposed approach based on the SODCC algorithm and the KLD constructs CNs with an emergent behaviour according to underlying wind speed prediction data physics, unlike the correlation-based method that produces spurious and missing links. Furthermore, it is shown that the climate network construction method facilitates the evaluation of symmetry properties in the resulting complex networks.

Multiplexity and multireciprocity in directed multiplexes

Real-world multilayer networks feature nontrivial dependencies among links of different layers. Here we argue that if links are directed, then dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of "multiplexity," there is also a tendency to antialign as a result of what we call "multireciprocity," i.e., the fact that links in one layer can be reciprocated by opposite links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the world trade multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is, however, largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow us to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness and complexity metrics.

Interactions between Financial and Environmental Networks in OECD Countries

We analysed a multiplex of financial and environmental networks between OECD countries from 2002 to 2010. Foreign direct investments and portfolio investment showing the flows in equity securities, short-term, long-term and total debt, these securities represent the financial layers; emissions of NOx, PM10, SO2, CO2 equivalent and the water footprint associated with international trade represent the environmental layers. We present a new measure of cross-layer correlations between flows in different layers based on reciprocity. For the assessment of results, we implement a null model for this measure based on the exponential random graph theory. We find that short-term financial flows are more correlated with environmental flows than long-term investments. Moreover, the correlations between reverse financial and environmental flows (i.e. the flows of different layers going in opposite directions) are generally stronger than correlations between synergic flows (flows going in the same direction). This suggests a trade-off between financial and environmental layers, where, more financialised countries display higher correlations between outgoing financial flows and incoming environmental flows than from lower financialised countries. Five countries are identified as hubs in this finance-environment multiplex: The United States, France, Germany, Belgium-Luxembourg and United Kingdom.

Network epidemiology and plant trade networks

Models of epidemics in complex networks are improving our predictive understanding of infectious disease outbreaks. Nonetheless, applying network theory to plant pathology is still a challenge. This overview summarizes some key developments in network epidemiology that are likely to facilitate its application in the study and management of plant diseases. Recent surveys have provided much-needed datasets on contact patterns and human mobility in social networks, but plant trade networks are still understudied. Human (and plant) mobility levels across the planet are unprecedented-there is thus much potential in the use of network theory by plant health authorities and researchers. Given the directed and hierarchical nature of plant trade networks, there is a need for plant epidemiologists to further develop models based on undirected and homogeneous networks. More realistic plant health scenarios would also be obtained by developing epidemic models in dynamic, rather than static, networks. For plant diseases spread by the horticultural and ornamental trade, there is the challenge of developing spatio-temporal epidemic simulations integrating network data. The use of network theory in plant epidemiology is a promising avenue and could contribute to anticipating and preventing plant health emergencies such as European ash dieback.

Spatial effects in real networks: measures, null models, and applications

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two factors can be varied arbitrarily, it is much more difficult to disentangle these two architectural effects in real networks. Here we propose a solution to this problem, by introducing global and local measures of spatial effects that, through a comparison with adequate null models, effectively filter out the spurious contribution of nonspatial constraints. Our filtering allows us to consistently compare different embedded networks or different historical snapshots of the same network. As a challenging application we analyze the World Trade Web, whose topology is known to depend on geographic distances but is also strongly determined by nonspatial constraints (degree sequence or gross domestic product). Remarkably, we are able to detect weak but significant spatial effects both locally and globally in the network, showing that our method succeeds in retrieving spatial information even when nonspatial factors dominate. We finally relate our results to the economic literature on gravity models and trade globalization.