Showing papers by "Tiziano Squartini published in 2018"

The Statistical Physics of Real-World Networks

Abstract: In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models for networks reproducing some features of real-world systems, but otherwise as random as possible. We review here the statistical physics approach and the various null models for complex networks, focusing in particular on the analytic frameworks reproducing the local network features. We then show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics models that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, as well as the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.

Reconstruction methods for networks: the case of economic and financial systems

Abstract: When studying social, economic and biological systems, one has often access to only limited information about the structure of the underlying networks. An example of paramount importance is provided by financial systems: information on the interconnections between financial institutions is privacy-protected, dramatically reducing the possibility of correctly estimating crucial systemic properties such as the resilience to the propagation of shocks. The need to compensate for the scarcity of data, while optimally employing the available information, has led to the birth of a research field known as network reconstruction. Since the latter has benefited from the contribution of researchers working in disciplines as different as mathematics, physics and economics, the results achieved so far are still scattered across heterogeneous publications. Most importantly, a systematic comparison of the network reconstruction methods proposed up to now is currently missing. This review aims at providing a unifying framework to present all these studies, mainly focusing on their application to economic and financial networks.

Entropy-based approach to missing-links prediction

Abstract: Link-prediction is an active research field within network theory, aiming at uncovering missing connections or predicting the emergence of future relationships from the observed network structure. This paper represents our contribution to the stream of research concerning missing links prediction. Here, we propose an entropy-based method to predict a given percentage of missing links, by identifying them with the most probable non-observed ones. The probability coefficients are computed by solving opportunely defined null-models over the accessible network structure. Upon comparing our likelihood-based, local method with the most popular algorithms over a set of economic, financial and food networks, we find ours to perform best, as pointed out by a number of statistical indicators (e.g. the precision, the area under the ROC curve, etc.). Moreover, the entropy-based formalism adopted in the present paper allows us to straightforwardly extend the link-prediction exercise to directed networks as well, thus overcoming one of the main limitations of current algorithms. The higher accuracy achievable by employing these methods - together with their larger flexibility - makes them strong competitors of available link-prediction algorithms.

Entropy-based approach to missing-links prediction

Abstract: Link-prediction is an active research field within network theory, aiming at uncovering missing connections or predicting the emergence of future relationships from the observed network structure. This paper represents our contribution to the stream of research concerning missing links prediction. Here, we propose an entropy-based method to predict a given percentage of missing links, by identifying them with the most probable non-observed ones. The probability coefficients are computed by solving opportunely defined null-models over the accessible network structure. Upon comparing our likelihood-based, local method with the most popular algorithms over a set of economic, financial and food networks, we find ours to perform best, as pointed out by a number of statistical indicators (e.g. the precision, the area under the ROC curve, etc.). Moreover, the entropy-based formalism adopted in the present paper allows us to straightforwardly extend the link-prediction exercise to directed networks as well, thus overcoming one of the main limitations of current algorithms. The higher accuracy achievable by employing these methods - together with their larger flexibility - makes them strong competitors of available link-prediction algorithms.

Colombian Export Capabilities: Building the Firms-Products Network

Abstract: In this paper, we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014. Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products. These clusters have been detected by running the bipartite variant of the traditional modularity maximization, revealing a bi-modular structure. Interestingly, this finding is refined by applying a recently proposed algorithm for projecting bipartite networks on the layer of interest and, then, running the Louvain algorithm on the resulting monopartite representations. Important structural differences emerge upon comparing the Colombian firms-products network with the World Trade Web, in particular, the bipartite representation of the latter is not characterized by a similar block-structure, as the modularity maximization fails in revealing (bipartite) nodes clusters. This points out that economic systems behave differently at different scales: while countries tend to diversify their production-potentially exporting a large number of different products-firms specialize in exporting (substantially very limited) baskets of basically homogeneous products.

A faster horse on a safer trail: generalized inference for the efficient reconstruction of weighted networks

Abstract: Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system (e.g. the implied level of systemic risk) requires detailed information about the structure of the underlying network. However, since data about financial linkages are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several "horse races" have been conducted to compare the performance of the available financial network reconstruction methods. These comparisons, however, were based on arbitrarily-chosen similarity metrics between the real and the reconstructed network. Here we establish a generalised maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization maximizes the conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved. The resulting approach admits as input any reconstruction method for the purely binary topology and, conditionally on the latter, exploits the available partial information to infer link weights. We find that the most reliable method is obtained by "dressing" the best-performing binary method with an exponential distribution of link weights having a properly density-corrected and link-specific mean value and propose two unbiased (in the sense of maximum conditional entropy) variants of it. While the one named CReMA is perfectly general (as a particular case, it can place optimal weights on a network whose topology is known), the one named CReMB is recommended both in case of full uncertainty about the network topology and if the existence of some links is certain. In these cases, the CReMB is faster and reproduces empirical networks with highest generalised likelihood.

Detecting Core-Periphery Structures by Surprise

Abstract: Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e. groups of nodes whose connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically-signifcant bimodular structures, i.e. either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) just between the (empty) layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional (binomial) hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.

From Ecology to Finance (and Back?): A Review on Entropy-Based Null Models for the Analysis of Bipartite Networks

Abstract: Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analyses of their topological structures have revealed the ubiquitous presence of properties which seem to characterize many—apparently different—systems. Nestedness, for example, has been observed in biological plant-pollinator as well as in country-product exportation networks. Due to the interdisciplinary character of complex networks, tools developed in one field, for example ecology, can greatly enrich other areas of research, such as economy and finance, and vice versa. With this in mind, we briefly review several entropy-based bipartite null models that have been recently proposed and discuss their application to real-world systems. The focus on these models is motivated by the fact that they show three very desirable features: analytical character, general applicability, and versatility. In this respect, entropy-based methods have been proven to perform satisfactorily both in providing benchmarks for testing evidence-based null hypotheses and in reconstructing unknown network configurations from partial information. Furthermore, entropy-based models have been successfully employed to analyze ecological as well as economic systems. As an example, the application of entropy-based null models has detected early-warning signals, both in economic and financial systems, of the 2007–2008 world crisis. Moreover, they have revealed a statistically-significant export specialization phenomenon of country export baskets in international trade, a result that seems to reconcile Ricardo’s hypothesis in classical economics with recent findings on the (empirical) diversification industrial production at the national level. Finally, these null models have shown that the information contained in the nestedness is already accounted for by the degree sequence of the corresponding graphs.

Reconstructing mesoscale network structures

Abstract: When facing complex mesoscale network structures, it is generally believed that (null) models encoding the modular organization of nodes must be employed. The present paper focuses on two block structures that characterize the mesoscale organization of many real-world networks, i.e. the bow-tie and the core-periphery ones. Our analysis shows that constraining the network degree sequence is often enough to reproduce such structures, as confirmed by model selection criteria as AIC or BIC. As a byproduct, our paper enriches the toolbox for the analysis of bipartite networks - still far from being complete. The aforementioned structures, in fact, partition the networks into asymmetric blocks characterized by binary, directed connections, thus calling for the extension of a recently-proposed method to randomize undirected, bipartite networks to the directed case.

Network-based indicators of Bitcoin bubbles.

Abstract: The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions.

Complexity in Neural and Financial Systems: From Time-Series to Networks

Abstract: When can a system be unambiguously defined as “complex”? Although many real-world systems are believed to bear the signature of complexity, the question above remains unanswered. Our special issue aims at contributing to this ongoing discussion by collecting a number of studies tackling two aspects of complexity that have recently gained increasing attention: the temporal one and the structural one.

Tackling Information Asymmetry in Networks: A New Entropy-Based Ranking Index

Abstract: Information is a valuable asset in socio-economic systems, a significant part of which is entailed into the network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant, systemic properties (e.g. the risk of contagion in a network of liabilities), agents capable of providing a better estimation of (otherwise) inaccessible network properties, ultimately have a competitive advantage. In this paper, we address the issue of quantifying the information asymmetry of nodes: to this aim, we define a novel index—InfoRank—intended to rank nodes according to their information content. In order to do so, each node ego-network is enforced as a constraint of an entropy-maximization problem and the subsequent uncertainty reduction is used to quantify the node-specific accessible information. We, then, test the performance of our ranking procedure in terms of reconstruction accuracy and show that it outperforms other centrality measures in identifying the “most informative” nodes. Finally, we discuss the socio-economic implications of network information asymmetry.

Network-based indicators of Bitcoin bubbles

Abstract: The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions.

Colombian export capabilities: building the firms-products network

Abstract: In this paper we analyse the bipartite Colombian firms-products network, throughout a period of five years, from 2010 to 2014 Our analysis depicts a strongly modular system, with several groups of firms specializing in the export of specific categories of products These clusters have been detected by running the bipartite variant of the traditional modularity maximization, revealing a bi-modular structure Interestingly, this finding is refined by applying a recently-proposed algorithm for projecting bipartite networks on the layer of interest and, then, running the Louvain algorithm on the resulting monopartite representations Important structural differences emerge upon comparing the Colombian firms-products network with the World Trade Web, in particular, the bipartite representation of the latter is not characterized by a similar block-structure, as the modularity maximization fails in revealing (bipartite) nodes clusters This points out that economic systems behave differently at different scales: while countries tend to diversify their production --potentially exporting a large number of different products-- firms specialize in exporting (substantially very limited) baskets of basically homogeneous products

Erratum: Estimating topological properties of weighted networks from limited information [Phys. Rev. E 92, 040802(R) (2015)].

Abstract: This corrects the article DOI: 10.1103/PhysRevE.92.040802.