Network evolution based on centrality

Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System

A nested structure is a structural feature that is conducive to system stability formed by the coevolution of biological species in mutualistic ecosystems The coopetition relationship and value flow between industrial sectors in the global value chain are similar to the mutualistic ecosystem in nature. That is, the global economic system is always changing to form one dynamic equilibrium after another. In this paper, a nestedness-based analytical framework is used to define the generalist and specialist sectors for the purpose of analyzing the changes in the global supply pattern. We study why the global economic system can reach a stable equilibrium, what the role of different sectors play in the steady status, and how to enhance the stability of the global economic system. In detail, the domestic trade network, export trade network and import trade network of each country are extracted. Then, an econometric model is designed to analyze how the microstructure of the production system affects a country's macroeconomic performance.

Emergence of hierarchy in networked endorsement dynamics

Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general mechanisms that explain the creation and endurance of such hierarchies are not well understood. We introduce a generative model for the dynamics of hierarchies using time-varying networks, in which new links are formed based on the preferences of nodes in the current network and old links are forgotten over time. The model produces a range of hierarchical structures, ranging from egalitarianism to bistable hierarchies, and we derive critical points that separate these regimes in the limit of long system memory. Importantly, our model supports statistical inference, allowing for a principled comparison of generative mechanisms using data. We apply the model to study hierarchical structures in empirical data on hiring patterns among mathematicians, dominance relations among parakeets, and friendships among members of a fraternity, observing several persistent patterns as well as interpretable differences in the generative mechanisms favored by each. Our work contributes to the growing literature on statistically grounded models of time-varying networks.

Link Prediction in Bipartite Nested Networks

Real networks typically studied in various research fields—ecology and economic complexity, for example—often exhibit a nested topology, which means that the neighborhoods of high-degree nodes tend to include the neighborhoods of low-degree nodes. Focusing on nested networks, we study the problem of link prediction in complex networks, which aims at identifying likely candidates for missing links. We find that a new method that takes network nestedness into account outperforms well-established link-prediction methods not only when the input networks are sufficiently nested, but also for networks where the nested structure is imperfect. Our study paves the way to search for optimal methods for link prediction in nested networks, which might be beneficial for World Trade and ecological network analysis.

Nestedness Maximization in Complex Networks through the Fitness-Complexity Algorithm

Nestedness refers to the structural property of complex networks that the neighborhood of a given node is a subset of the neighborhoods of better-connected nodes. Following the seminal work by Patterson and Atmar (1986), ecologists have been long interested in revealing the configuration of maximal nestedness of spatial and interaction matrices of ecological communities. In ecology, the BINMATNEST genetic algorithm can be considered as the state-of-the-art approach for this task. On the other hand, the fitness-complexity ranking algorithm has been recently introduced in the economic complexity literature with the original goal to rank countries and products in World Trade export networks. Here, by bringing together quantitative methods from ecology and economic complexity, we show that the fitness-complexity algorithm is highly effective in the nestedness maximization task. More specifically, it generates matrices that are more nested than the optimal ones by BINMATNEST for 61.27% of the analyzed mutualistic networks. Our findings on ecological and World Trade data suggest that beyond its applications in economic complexity, the fitness-complexity algorithm has the potential to become a standard tool in nestedness analysis.

Revealing in-block nestedness: Detection and benchmarking

As new instances of nested organization-beyond ecological networks-are discovered, scholars are debating the coexistence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of in-block nestedness, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge.

Analysing the sensitivity of nestedness detection methods

Many bipartite and unipartite real-world networks display a nested structure. Examples pervade different disciplines: biological ecosystems (e.g. mutualistic networks), economic networks (e.g. manufactures and contractors networks) to financial networks (e.g. bank lending networks), etc. A nested network has a topology such that a vertex's neighbourhood contains the neighbourhood of vertices of lower degree; thus -upon vertex reordering- the adjacency matrix is step-wise. Despite its strict mathematical definition and the interest triggered by their common occurrence, it is not easy to measure the extent of nested graphs unequivocally. Among others, there exist three methods for detection and quantification of nestedness that are widely used: BINMATNEST, NODF, and fitness-complexity metric (FCM). However, these methods fail in assessing the existence of nestedness for graphs of low (NODF) and high (NODF, BINMATNEST) network density. Another common shortcoming of these approaches is the underlying assumption that all vertices belong to a nested component. However, many real-world networks have solely a sub-component (i.e. a subset of its vertices) that is nested. Thus, unveiling which vertices pertain to the nested component is an important research question, unaddressed by the methods available so far. In this contribution, we study in detail the algorithm Nestedness detection based on Local Neighbourhood (NESTLON). This algorithm resorts solely on local information and detects nestedness on a broad range of nested graphs independently of their nature and density. Further, we introduce a benchmark model that allows us to tune the degree of nestedness in a controlled manner and study the performance of different algorithms. Our results show that NESTLON outperforms both BINMATNEST and NODF.

Prebiotic network evolution: six key parameters

Akin to biological networks, prebiotic chemical networks can evolve and we have identified six key parameters that govern their evolution.

The role of endogenous and exogenous mechanisms in the formation of R&D networks

We develop an agent-based model of strategic link formation in Research and Development (R&D) networks. Empirical evidence has shown that the growth of these networks is driven by mechanisms which are both endogenous to the system (that is, depending on existing alliances patterns) and exogenous (that is, driven by an exploratory search for newcomer firms). Extant research to date has not investigated both mechanisms simultaneously in a comparative manner. To overcome this limitation, we develop a general modeling framework to shed light on the relative importance of these two mechanisms. We test our model against a comprehensive dataset, listing cross-country and cross-sectoral R&D alliances from 1984 to 2009. Our results show that by fitting only three macroscopic properties of the network topology, this framework is able to reproduce a number of micro-level measures, including the distributions of degree, local clustering, path length and component size, and the emergence of network clusters. Furthermore, by estimating the link probabilities towards newcomers and established firms from the data, we find that endogenous mechanisms are predominant over the exogenous ones in the network formation, thus quantifying the importance of existing structures in selecting partner firms.

Spontaneous centralization of control in a network of company ownerships

We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected “core” made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive “rich get richer” dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.