arXiv subjects

Tiziano Squartini

Publications and source records attributed to Tiziano Squartini.

At least 55 records · Page 3Linked to original sources

arXiv2020

Bitcoin Transaction Networks: an overview of recent results

Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens among participants. The complete historical bookkeeping and its wide availability opens up an unprecedented possibility, i.e. that of understanding the evolution of their network structure while gaining useful insight on the relationships between user' behaviour and cryptocurrency pricing in exchange markets. In this contribution we review some of the most recent results concerning the structural properties of Bitcoin Transaction Networks, a generic name referring to a set of different constructs: the Bitcoin Address Network, the Bitcoin User Network and the Bitcoin Lightning Network. The picture that emerges is that of system growing over time, which becomes increasingly sparse and whose mesoscopic structural organization is characterised by the presence of an increasingly significant core-periphery structure. Such a peculiar topology is matched by a highly uneven distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralized system at different levels.

physics.soc-ph↗

arXiv2020

Lightning Network: a second path towards centralisation of the Bitcoin economy

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.

physics.soc-ph↗

arXiv2020

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

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.

physics.soc-ph↗

arXiv2019

The Statistical Physics of Real-World Networks

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.

physics.soc-ph↗

arXiv2019

The evolving liaisons between the transaction networks of Bitcoin and its price dynamics

Cryptocurrencies are distributed systems that allow exchanges of native tokens among participants, or the exchange of such tokens for fiat currencies in markets external to these public ledgers. The availability of their complete historical bookkeeping opens up the possibility of understanding the relationship between aggregated users' behaviour and the cryptocurrency pricing in exchange markets. This paper analyses the properties of the transaction network of Bitcoin. We consider four different representations of it, over a period of nine years since the Bitcoin creation and involving 16 million users and 283 million transactions. By analysing these networks, we show the existence of causal relationships between Bitcoin price movements and changes of its transaction network topology. Our results reveal the interplay between structural quantities, indicative of the collective behaviour of Bitcoin users, and price movements, showing that, during price drops, the system is characterised by a larger heterogeneity of nodes activity.

q-fin.GN↗

arXiv2019

Detecting Core-Periphery Structures by Surprise

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.

physics.soc-ph↗

arXiv2018

Reconstructing mesoscale network structures

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.

physics.soc-ph↗

arXiv2018

Estimating topological properties of weighted networks from limited information

A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to reconstruct the structural properties of complex weighted networks of this kind using only partial information: the total number of nodes and links, and the values of the strength for all nodes. The latter are used as fitness to estimate the unknown node degrees through a standard configuration model. Then, these estimated degrees and the strengths are used to calibrate an enhanced configuration model in order to generate ensembles of networks intended to represent the real system. The method, which is tested on real economic and financial networks, while drastically reducing the amount of information needed to infer network properties, turns out to be remarkably effective$-$thus representing a valuable tool for gaining insights on privacy-protected socioeconomic systems.

physics.soc-ph↗

arXiv2018

Colombian export capabilities: building the firms-products network

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.

physics.soc-ph↗

arXiv2018

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

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.

physics.soc-ph↗

arXiv2018

Entropy-based approach to missing-links prediction

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.

physics.soc-ph↗

arXiv2018

Network-based indicators of Bitcoin bubbles

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.

physics.soc-ph↗

arXiv2017

Reconnecting statistical physics and combinatorics beyond ensemble equivalence

In statistical physics, the challenging combinatorial enumeration of the configurations of a system subject to hard constraints (microcanonical ensemble) is mapped to a mathematically easier calculation where the constraints are softened (canonical ensemble). However, the mapping is exact only when the size of the system is infinite and if the property of ensemble equivalence (EE), i.e. the asymptotic identity of canonical and microcanonical large deviations, holds. For finite systems, or when EE breaks down, statistical physics is currently believed to provide no answer to the combinatorial problem. In contrast with this expectation, here we establish exact relationships connecting conjugate ensembles in full generality, even for finite system size and when EE does not hold. We also show that in the thermodynamic limit the ensembles are directly related through the matrix of canonical (co)variances of the constraints, plus a correction term that survives only if this matrix has an infinite number of finite eigenvalues. These new relationships restore the possibility of enumerating microcanonical configurations via canonical probabilities, thus reconnecting statistical physics and combinatorics in realms where they were believed to be no longer in mutual correspondence.

cond-mat.stat-mech↗

arXiv2017

From Ecology to Finance (and Back?): Recent Advancements in the Analysis of Bipartite Networks

Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analysis of their topological structures has revealed the ubiquitous presence of properties which seem to characterize many - apparently different - systems. Nestedness, for example, has been observed in plants-pollinator as well as in country-product trade networks. This has raised questions about the significance of these patterns, which are often believed to constitute a genuine signature of self-organization. Here, we review several methods that have been developed for the analysis of such evidence. 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 several 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. On top of that, entropy-based models have been successfully employed to analyze ecological as well as economic systems, thus representing an ideal, interdisciplinary tool to approach the study of bipartite complex systems. [...]

physics.soc-ph↗

arXiv2017

Tackling information asymmetry in networks: a new entropy-based ranking index

Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very 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 financial contagion in a network of liabilities), agents capable of providing a better estimate of (otherwise) unaccessible network properties, ultimately have a competitive advantage. In this paper, we address for the first time the issue of quantifying the information asymmetry arising from the network topology. To this aim, we define a novel index - InfoRank - intended to measure the quality of the information possessed by each node, computing the Shannon entropy of the ensemble conditioned on the node-specific information. Further, we test the performance of our novel ranking procedure in terms of the reconstruction accuracy of the (unaccessible) network structure and show that it outperforms other popular centrality measures in identifying the "most informative" nodes. Finally, we discuss the socio-economic implications of network information asymmetry.

cs.SI↗

arXiv2017

Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks

Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets is strongly affected by the interconnections among financial institutions. Yet, while the aggregate balance sheets of institutions are publicly disclosed, information on single positions is mostly confidential and, as such, unavailable. Standard approaches to reconstruct the network of financial interconnection produce unrealistically dense topologies, leading to a biased estimation of systemic risk. Moreover, reconstruction techniques are generally designed for monopartite networks of bilateral exposures between financial institutions, thus failing in reproducing bipartite networks of security holdings (\eg, investment portfolios). Here we propose a reconstruction method based on constrained entropy maximization, tailored for bipartite financial networks. Such a procedure enhances the traditional {\em capital-asset pricing model} (CAPM) and allows to reproduce the correct topology of the network. We test this ECAPM method on a dataset, collected by the European Central Bank, of detailed security holdings of European institutional sectors over a period of six years (2009-2015). Our approach outperforms the traditional CAPM and the recently proposed MECAPM both in reproducing the network topology and in estimating systemic risk due to fire-sales spillovers. In general, ECAPM can be applied to the whole class of weighted bipartite networks described by the fitness model.

q-fin.RM↗

arXiv2017

Inferring monopartite projections of bipartite networks: an entropy-based approach

Bipartite networks are currently regarded as providing a major insight into the organization of many real-world systems, unveiling the mechanisms driving the interactions occurring between distinct groups of nodes. One of the most important issues encountered when modeling bipartite networks is devising a way to obtain a (monopartite) projection on the layer of interest, which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated projections of bipartite networks, according to which any two nodes sharing a statistically-significant number of neighbors are linked. Since assessing the statistical significance of nodes similarity requires a proper statistical benchmark, here we consider a set of four null models, defined within the exponential random graph framework. Our algorithm outputs a matrix of link-specific p-values, from which a validated projection is straightforwardly obtainable, upon running a multiple hypothesis testing procedure. Finally, we test our method on an economic network (i.e. the countries-products World Trade Web representation) and a social network (i.e. MovieLens, collecting the users' ratings of a list of movies). In both cases non-trivial communities are detected: while projecting the World Trade Web on the countries layer reveals modules of similarly-industrialized nations, projecting it on the products layer allows communities characterized by an increasing level of complexity to be detected; in the second case, projecting MovieLens on the films layer allows clusters of movies whose affinity cannot be fully accounted for by genre similarity to be individuated.

physics.soc-ph↗

arXiv2016

Network reconstruction via density sampling

Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to reliably replicate the empirical degree sequence, which is however unknown in many realistic situations. More recently, it has been found that the knowledge of the degree sequence can be replaced by the knowledge of the strength sequence, which is typically accessible, complemented by that of the total number of links, thus considerably relaxing the observational requirements. Here we further relax these requirements and devise a procedure valid when even the the total number of links is unavailable. We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density. We show that the best way of sampling nodes is the random selection scheme, any other procedure being biased towards unrealistically large, or small, link densities. We then introduce our core technique for reconstructing both the topology and the link weights of the unknown network in detail. When tested on real economic and financial data sets, our method achieves a remarkable accuracy and is very robust with respect to the sampled subsets, thus representing a reliable practical tool whenever the available topological information is restricted to small portions of nodes.

physics.soc-ph↗