Dr. Diego Garlaschelli Assistant Professor Lorentz Institute for Theoretical Physics Leiden Institute of Physics University of Leiden P.O. Box 9506, NL-2300 RA Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands
Born in Rome (25/11/1977). Male, married (19/06/2004), one son (19/03/2009), one daughter (23/06/2010).
EDUCATION:
2001: Degree in Physics, Third University of Rome (Italy). “Proprietà Statistiche e di Auto-Organizzazione nelle Reti Ecologiche Complesse” Supervisor: Prof. Luciano Pietronero (Mark: 110/110)
2005: Phd in Physics, University of Siena (Italy). “Statistical Physics Approach to the Topology and Dynamics of Complex Networks”. Supervisor: Prof. Maria I. Loffredo
POST-DOCTORAL RESEARCH POSITIONS:
2005: Visiting Fellow, Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, (Australia).
2005: Research Contract, Physics Department, University of Siena (Italy).
2005: Research Contract, Italian National Research Council (CNR), Institute of Complex Systems (ISC), Rome (Italy).
2005-2009: Research Fellow and Lecturer, Physics Department, University of Siena (Italy).
2009-2010: Research Fellow, CABDyN Complexity Center, Said Business School, University of Oxford (UK).
2009-2010: Research Associate, Green Templeton College, University of Oxford (UK).
2010-2011: Research Fellow, Laboratory of Economics and Management, Sant'Anna School of Advanced Studies, Pisa (Italy)
TEACHING ACTIVITY
at the University of Siena:
- Probabilistic Models (Postgraduate course in BioInformatics): 2003 - 2010. - Physics (Bachelor Degree in Pharmacy): 2004 - 2009. - Structure of Matter II (Masters Degree in Physics): 2005 - 2006. - Statistical Mechanics (Bachelor Degree in Physics): 2007. - Physics of Complex Systems (Masters Degree in Physics): 2006 - 2009. - Network Theory and Complexity (PhD course): 2011. - Organizing responsible of the Multidisciplinary PhD Program “Physics and Complex Systems” and the associated chair in “Econophysics”: 2008-2011.
at the University of Leiden:
- Econophysics (Bachelor Degree in Physics): 2011 - present.
REFEREE OF INTERNATIONAL JOURNALS:
Nature, Physical Review Letters, Physical Review E, New Journal of Physics, EuroPhysics Letters, European Physical Journal B, Physica A, Journal of Physics A, Journal of Statistical Mechanics, Physics Letters, Advances in Complex Systems, BioMed Central Systems Biology, BioMed Central Bioinformatics, Ecological Modelling, Journal of Economic Behaviour and Organization, Social Networks, Industrial and Corporate Change.
INVITED TALKS:
- January-February 2006: Interfacing Networks: from behavioural Networks to info-structures and infrastructures, ISI Foundation, Torino (Italy).
- September, 2006: Third International School of Complexity on “Physics and Socio-Economics Phenomena”, Erice (Italy).
- September 2006: Workshop on Social and Ecological Networks, European Conference on Complex Systems (ECCS 2006), Oxford (UK).
- June 2008: CREEN Symposium - Satellite event for NetSci08 - Norwich (UK).
- September 2008: Dynamics Days Asia Pacific, Nara (Japan).
- September 2008: NetAce Conference, Brunel University, West London (UK).
- September 2009: BioPhys09: Biology and Beyond, Arcidosso (Italy).
- October 2009: Energy Growth, Efficiency and Complexity, Siena University (Italy).
- September 2010: Science of Complex Networks (SCNET 2010) - Satellite event for the European Conference on Complex Systems (ECCS 2010), Lisbon (Portugal).
- February 2011: Network Theory and Complexity, Siena University (Italy).
- March 2011: Postgraduate School on “Statistical Physics and Theory of Condensed Matter”, Driebergen-Rijsenburg (The Netherlands).
- March 2011: Workshop "Networks constrained to change", Green Templeton College, University of Oxford (UK).
- July 2011: Sigma Phi 2011 - International Conference on Statistical Physics (Cyprus).
MEMBER OF SCIENTIFIC COMMITTEES OF INTERNATIONAL CONFERENCES:
- May 2008: Third International Workshop of Emergent Intelligence on Networked Agents WEIN’08, (Estoril, Portugal).
- December 2008: Joint Conference of the 2008 Winter Workshop on Economics with Heterogeneous Interacting Agents and the 7th International Conference on Computational Intelligence in Economics and Finance, Kainan University, (Taoyuan, Taiwan).
- February 2009: Complex’2009 - First International Conference on Complex Sciences: Theory and Applications (Shangai, China).
- June/July 2010: International School on Multidisciplinary Approaches to Economic and Social Complex Systems (Siena, Italy).
INTERNATIONAL PRIZES/AWARDS:
-September 2003: best talk presented by young researchers at the “Second International Conference on Frontier Science ‘a Nonlinear World: the Real World’”, Pavia (Italy), Collegio Cairoli.
-September 2004: best talk presented by young researchers at the “First Bonzenfreies Colloquium on Market Dynamics and Quantitative Economics”, Alessandria (Italy), Hotel Lux.
Abstract: An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and long-term cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are intensively studied, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that interopinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space. When empirical data are used as inputs in models, ultrametricity has strong and counterintuitive effects. On short timescales, it facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long timescales, it suppresses cultural convergence by restricting it within disjoint groups. Moreover, ultrametricity implies that these results are surprisingly robust to modifications of the dynamical rules considered. Thus the empirical distribution of individuals in cultural space appears to systematically optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence in a diverse range of online and offline settings.
Abstract: In all empirical-network studies, the observed properties of economic networks are informative only if compared with a well-defined null model that can quantitatively predict the behavior of such properties in constrained graphs. However, predictions of the available null-model methods can be derived analytically only under assumptions (e.g., sparseness of the network) that are unrealistic for most economic networks like the World Trade Web (WTW). In this paper we study the evolution of the WTW using a recently-proposed family of null network models. The method allows to analytically obtain the expected value of any network statistic across the ensemble of networks that preserve on average some local properties, and are otherwise fully random. We compare expected and observed properties of the WTW in the period 1950-2000, when either the expected number of trade partners or total country trade is kept fixed and equal to observed quantities. We show that, in the binary WTW, node-degree sequences are sufficient to explain higher-order network properties such as disassortativity and clustering-degree correlation, especially in the last part of the sample. Conversely, in the weighted WTW, the observed sequence of total country imports and exports are not sufficient to predict higher-order patterns of the WTW. We discuss some important implications of these findings for international-trade models.
Abstract: One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of triangles in which edges, rather than vertices, participate. Here we show that the multiplicity distribution of real networks is in many cases scale free, and in general very broad. Thus, besides the fact that in real networks the number of edges attached to vertices often has a scale-free distribution, we find that the number of triangles attached to edges can have a scale-free distribution as well. We show that current models, even when they generate clustered networks, systematically fail to reproduce the observed multiplicity distributions. We therefore propose a generalized model that can reproduce networks with arbitrary distributions of vertex degrees and edge multiplicities, and study many of its properties analytically.
Abstract: Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed and undirected, aggregated and disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.
Abstract: The international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary or weighted, directed or undirected, aggregated or disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.
Abstract: In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, the generation of them is still problematic. Existing approaches are either computationally demanding and beyond analytic control or analytically accessible but highly approximate. Here, we propose a solution to this long-standing problem by introducing a fast method that allows one to obtain expectation values and standard deviations of any topological property analytically, for any binary, weighted, directed or undirected network. Remarkably, the time required to obtain the expectation value of any property analytically across the entire graph ensemble is as short as that required to compute the same property using the adjacency matrix of the single original network. Our method reveals that the null behavior of various correlation properties is different from what was believed previously, and is highly sensitive to the particular network considered. Moreover, our approach shows that important structural properties (such as the modularity used in community detection problems) are currently based on incorrect expressions, and provides the exact quantities that should replace them.
Abstract: We study the topological properties of the multinetwork of commodity-specific trade relations among world countries over the 1992â2003 period, comparing them with those of the aggregate-trade network, known in the literature as the international-trade network (ITN). We show that link-weight distributions of commodity-specific networks are extremely heterogeneous and (quasi) log normality of aggregate link-weight distribution is generated as a sheer outcome of aggregation. Commodity-specific networks also display average connectivity, clustering, and centrality levels very different from their aggregate counterpart. We also find that ITN complete connectivity is mainly achieved through the presence of many weak links that keep commodity-specific networks together and that the correlation structure existing between topological statistics within each single network is fairly robust and mimics that of the aggregate network. Finally, we employ cross-commodity correlations between link weights to build hierarchies of commodities. Our results suggest that on the top of a relatively time-invariant âintrinsicâ taxonomy (based on inherent between-commodity similarities), the roles played by different commodities in the ITN have become more and more dissimilar, possibly as the result of an increased trade specialization. Our approach is general and can be used to characterize any multinetwork emerging as a nontrivial aggregation of several interdependent layers.
Abstract: Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non-linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass-metabolism allometric exponent b = 0.75, activation energy range 0.2â1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best-supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best-supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non-linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.
Abstract: In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.
Abstract: We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.
Abstract: For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real-world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich-club coefficient to weighted networks which is complementary to other recently proposed ones.
Abstract: We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the ErdosâRenyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is characterized by a geometric weight distribution, a binomial degree distribution and a negative binomial strength distribution. We also characterize exactly the percolation phase transitions associated with edge removal and with the appearance of weighted subgraphs of any order and intensity. We find that even this completely null model displays a percolation behaviour similar to what is observed in real weighted networks, implying that edge removal cannot be used to detect community structure empirically. By contrast, the analysis of clustering successfully reveals different patterns between the WRG and real networks.
Notes: Online Wolfram Demonstration by T. Squartini available at http://demonstrations.wolfram.com/WeightedRandomGraph/
Abstract: We derive a class of generalized statistics, unifying the Bose and Fermi ones, that describe any system where the first-occupation energies or probabilities are different from subsequent ones, as in the presence of thresholds, saturation, or aging. The statistics completely describe the structural correlations of weighted networks, which turn out to be stronger than expected and to determine significant topological biases. Our results show that the null behavior of weighted networks is different from what was previously believed, and that a systematic redefinition of weighted properties is necessary.
Abstract: In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two datasets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.
Abstract: The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the maximum likelihood (ML) principle indicates a unique, statistically rigorous parameter choice, associated with a well-defined topological feature. We then find that, if the ML condition is incompatible with the built-in parameter choice, network models turn out to be intrinsically ill defined or biased. To overcome this problem, we construct a class of safely unbiased models. We also propose an extension of these results that leads to the fascinating possibility to extract, only from topological data, the âhidden variablesâ underlying network organization, making them âno longer hidden.â We test our method on World Trade Web data, where we recover the empirical gross domestic product using only topological information.
Abstract: We analyze several florae (collections of plant species populating specific areas) in different geographic and climatic regions. For every list of species we produce a taxonomic classification tree and we consider its statistical properties. We find that regardless of the geographical location, the climate and the environment all species collections have universal statistical properties that we show to be also robust in time. We then compare observed data sets with simulated communities obtained by randomly sampling a large pool of species from all over the world. We find differences in the behavior of the statistical properties of the corresponding taxonomic trees. Our results suggest that it is possible to distinguish quantitatively real species assemblages from random collections and thus demonstrate the existence of correlations between species.
Abstract: Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed [1] self-organized model for the evolution of complex networks. Vertices of the network are characterized by a fitness variable evolving through an extremal dynamics process, as in the Bak-Sneppen [2] model representing a prototype of Self-Organized Criticality. The network topology is in turn shaped by the fitness variable itself, as in the fitness network model [3]. The system self-organizes to a nontrivial state, characterized by a power-law decay of dynamical and topological quantities above a critical threshold. The interplay between topology and dynamics in the system is the key ingredient leading to an unexpected behaviour of these quantities.
Abstract: We focus on the problem of how the wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of the log-normal and power-law behaviours. We then focus on the Bouchaud-Mezard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self-organizes towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular, we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log-normal or the power-law form. This means that the first-order topological properties alone (such as the scale-free property) are not enough to explain the emergence of the empirically observed mixed form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with a variable density of links. We show new results detailing how this effect is related to the higher-order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other.
Abstract: We present an empirical analysis of the network formed by the trade relationships between all world countries, or World Trade Web (WTW). Each (directed) link is weighted by the amount of wealth flowing between two countries, and each country is characterized by the value of its Gross Domestic Product (GDP). By analysing a set of year-by-year data covering the time interval 1950-2000, we show that the dynamics of all GDP values and the evolution of the WTW (trade flow and topology) are tightly coupled. The probability that two countries are connected depends on their GDP values, supporting recent theoretical models relating network topology to the presence of a âhiddenâ variable (or fitness). On the other hand, the topology is shown to determine the GDP values due to the exchange between countries. This leads us to a new framework where the fitness value is a dynamical variable determining, and at the same time depending on, network topology in a continuous feedback.
Abstract: The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a âfitnessâ, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.
Abstract: We present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the nearest neighbors, the clustering coefficient, the âbetweenness,â the distance between two nodes, and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Our approach is based on the translation of a weighted network into an ensemble of edges. Further introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.
Abstract: Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grand-canonical class of models reproducing the observed patterns of reciprocity by regarding single and double links as Fermi particles of different âchemical speciesâ governed by the corresponding chemical potentials. Within this framework we find interesting special cases such as the extensions of random graphs, the configuration model, and hidden-variable models. Our theoretical predictions are also in excellent agreement with the empirical results for networks with well-studied reciprocity.
Abstract: The World Trade Web (WTW), the network defined by the international import/export trade relationships, has been recently shown to display some important topological properties which are tightly related to the Gross Domestic Product of world countries. While our previous analysis focused on the static, undirected version of the WTW, here we address its full evolving, directed description. This is accomplished by exploiting the peculiar reciprocity structure of the WTW to recover the directed nature of international trade channels, and by studying the temporal dependence of the parameters describing the WTW topology. (c) 2005 Elsevier B.V. All rights reserved.
Abstract: We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree (k(in)) and the sum of incoming link weights (nu) of an investor correspond to the number of assets held (portfolio diversification) and to the invested wealth (portfolio volume), respectively. An empirical analysis of three different real markets reveals that the distributions of both k(in), and nu display power-law tails with exponents gamma and alpha. Moreover, we find that k(in), scales as a power-law function of nu with an exponent beta. Remarkably, despite the values of alpha, beta and gamma differ across the three markets, they are always governed by the scaling relation beta = (1 - alpha)/(1 - gamma). We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of âhiddenâ vertex properties. (c) 2004 Elsevier B.V. All rights reserved.
Abstract: Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations, and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.
Abstract: We address the problem of link reciprocity, the nonrandom presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.
Abstract: We study a model of wealth dynamics (Physica A 282 (2000) 536) which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a fully disconnected network yield power-law and log-normal forms of the wealth distribution, respectively. We perform numerical simulations in order to test the model on more complex network topologies. We show that the mixed form of most empirical distributions (displaying a non-smooth transition from a log-normal to a power-law form) can be traced back to a heterogeneous topology with varying link density, which on the other hand is a recently observed property of real networks. (C) 2004 Elsevier B.V. All rights reserved.
Abstract: Among recently studied real-world networks, food webs are particularly interesting since they provide an example of biological organization at the largest scale, namely that of ecological communities. Quite surprisingly, recent results reveal that food webs do not display those properties which are observed in almost all other networks, such as a scale-free degree distribution and a large clustering coefficient. However, when food webs are regarded from the point of view of trasportation networks, it is possible to uncover very interesting scaling properties which are displayed by other trasportation systems, namely vascular and river networks. While other topological properties appear to vary across different webs depending on specific aspects, such scaling relations are universal. An interpretation of these results in terms of the interplay of universal and nonuniversal mechanisms in food web evolution is suggested.
Abstract: The structure of ecological communities is usually represented by food webs(1-3). In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks(4,5). Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs(1-3,6) are different from those found in large ones(7-15). Furthermore, food webs (except in isolated cases(16,17)) do not share(18,19) general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character(4,5) and a scale-free (power-law) distribution of the degree(4,5) (the number of links per vertex). Here we propose to describe food webs as transportation networks(20) by extending to them the concept of allometric scaling(20-22) (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.
Abstract: The World Trade Web (WTW) is the complex network representation of the international trade system that allows an analysis at the large scale from an interdisciplinary approach. Countries are represented as nodes and commercial relations between them as links. The network representation offers a new level of description that goes beyond the country-specific analyses used in more traditional economic studies of trade. In particular, it makes possible the analysis of the indirect trade interactions among world countries. In this line of research, several tools and methodologies that have been recently developed for the analysis of any type of networks can be exploited to extract information from the WTW, and to discriminate which properties signal a nontrivial structural organization and which are likely to be originated by chance or structural constraints. Although these results have been obtained recently, and during a relatively short period of time, they have already established various robust empirical signatures of the international trade network. In some cases, these âstylized factsâ turn out to be stable in time, while in others they highlight previously unrecognized changes in the system. We present a self-contained description of these advances. After a general introduction to the international trade system, we describe the possible representations of the WTW that have appeared in the literature, from its purely topological properties to its weighted structure and directionality, and the added levels of understanding they convey. We then describe various models that have been proposed to reproduce the empirical properties of the WTW, from more traditional âgravity modelsâ which predict expected trade volumes but cannot reproduce the topology of the web, to recent network-inspired models that succeed in explaining the observed complexity of the network at a topological level. We finally discuss some open questions for future research on the world trade system as a complex network.
Abstract: We present here an overview of the use of networks in Finance and Economics. We show how this approach enables us to address important questions as, for example, the structure of control chains in financial systems, the systemic risk associated with them and the evolution of trade between nations. All these results are new in the field and allow for a better understanding and modelling of different economic systems.
Abstract: In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. (Nat. Phys. 3: 813, 2007) that couples the fitness network model defined by Caldarelli et al. (Phys. Rev. Lett. 89: 258702, 2002) with the evolution model proposed by Bak and Sneppen (Phys. Rev. Lett. 71: 4083, 1993) as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.
Abstract: We study the statistical properties of the network of shareholding relationships in the Italian stock market (MIB) and in two US stock markets (NYSE and NASDAQ). The networks are found to be scale free a feature which doesn't seem to be in accord with classical theories of portfolio optimization. Several statistical properties differ across markets and allow for a classification. We introduce two quantities, HI and SI, analogous to in-degree and out-degree for weighted graphs. The distribution of HI and SI allow us to characterize from a statistical perspective the individual ownership concentration of stocks and the individual power of holders. They also suggest two different global pictures of the structure of the networks: the MIB seems characterized by medium size holders controlling separate subsets of stocks, while the US markets seem characterized by very large holders sharing control over subsets of stocks.
Abstract: We present here a brief summary of the various possible applications of network theory in the field of finance. Since we want to characterize different systems by means of simple and universal features, graph theory could represent a rather powerful methodology. In the following we report our activity in three different subfields, namely the board and director networks, the networks formed by prices correlations and the stock ownership networks. In most of the cases these three kind of networks display scale-free properties making them interesting in their own. Nevertheless, we want to stress here that the main utility of this methodology is to provide new measures of the real data sets in order to validate the different models.
Abstract: In addition to traditional properties such as the degree distribution P( k), in this work we propose two other useful quantities that can help in characterizing the topology of food webs quantitatively, namely the allometric scaling relations C( A) and the branch size distribution P(A) A which are defined on the spanning tree of the webs. These quantities, whose use has proved relevant in characterizing other different networks appearing in nature (such as river basins, Internet, and vascular systems), are related (in the context of food webs) to the efficiency in the resource transfer and to the stability against species removal. We present the analysis of the data for both real food webs and numerical simulations of a growing network model. Our results allow us to conclude that real food webs display a high degree of both efficiency and stability due to the evolving character of their topology.
