arXiv subjects

Ginestra Bianconi

Publications and source records attributed to Ginestra Bianconi.

At least 127 records · Page 7Linked to original sources

arXiv2015

Emergent Complex Network Geometry

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.

physics.soc-ph↗

arXiv2015

Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles

Spatial networks range from the brain networks, to transportation networks and infrastructures. Recently interacting and multiplex networks are attracting great attention because their dynamics and robustness cannot be understood without treating at the same time several networks. Here we present maximal entropy ensembles of spatial multiplex and spatial interacting networks that can be used in order to model spatial multilayer network structures and to build null models of real datasets. We show that spatial multiplex naturally develop a significant overlap of the links, a noticeable property of many multiplexes that can affect significantly the dynamics taking place on them. Additionally, we characterize ensembles of spatial interacting networks and we analyse the structure of interacting airport and railway networks in India, showing the effect of space in determining the link probability.

physics.soc-ph↗

arXiv2015

Statistical mechanics of random geometric graphs: Geometry-induced first order phase transition

Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables model and apply the resulting equations to RGG. For any RGG, defined through a rigid or a soft geometric rule, the method reduces to a non trivial satisfaction problem: Given $N$ nodes, a domain $\mathcal{D}$, and a desired average connectivity $\langle k\rangle$, find - if any - the distribution of nodes having support in $\mathcal{D}$ and average connectivity $\langle k\rangle$. We find out that, in the thermodynamic limit, nodes are either uniformly distributed or highly condensed in a small region, the two regimes being separated by a first order phase transition characterized by a $\mathop{O}(N)$ jump of $\langle k\rangle$. Other intermediate values of $\langle k\rangle$ correspond to very rare graph realizations. The phase transition is observed as a function of a parameter $a\in[0,1]$ that tunes the underlying geometry. In particular, $a=1$ indicates a rigid geometry where only close nodes are connected, while $a=0$ indicates a rigid anti-geometry where only distant nodes are connected. Consistently, when $a=1/2$ there is no geometry and no phase transition. After discussing the numerical analysis, we provide a combinatorial argument to fully explain the mechanism inducing this phase transition and recognize it as an easy-hard-easy transition. Our result shows that, in general, ad hoc optimized networks can hardly be designed, unless to rely to specific heterogeneous constructions, not necessarily scale free.

cond-mat.dis-nn↗

arXiv2015

Emergence of Soft Communities from Geometric Preferential Attachment

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.

physics.soc-ph↗

arXiv2015

Supersymmetric multiplex networks described by coupled Bose and Fermi statistics

Until now, no simple symmetries have been detected in complex networks. Here we show that, in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglement entropy to the layers of multiplex networks. Interestingly we observe a very simple relation between the entanglement entropies of the layers of the supersymmetric multiplex network and the entropy rate of the same multiplex network. This relation therefore connects the classical non equilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.

cond-mat.dis-nn↗

arXiv2014

Mutually connected component of network of networks with replica nodes

We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove that if in these networks, all the nodes of one network (layer) are interdependent on the nodes of the same other interconnected layer, then, remarkably, the mutually connected component does not depend on the topology of the network of networks. This component coincides with the mutual component of the fully connected network of networks constructed from the same set of layers, i.e., a multiplex network.

physics.soc-ph↗

arXiv2014

Correlations between weights and overlap in ensembles of weighted multiplex networks

Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also weighted, and the weights of the links can be strongly correlated with the structural properties of the multiplex network. For example in multiplex network formed by the citation and collaboration networks between PRE scientists it was found that the statistical properties of citations to co-authors are different from the one of citations to non-co-authors, i.e. the weights depend on the overlap of the links. Here we present a theoretical framework for modelling multiplex weighted networks with different types of correlations between weights and overlap. To this end, we use the framework of canonical network ensembles, and the recently introduced concept of multilinks, showing that null models of a large variety of network structures can be constructed in this way. In order to provide a concrete example of how this framework apply to real data we consider a multiplex constructed from gene expression data of healthy and cancer tissues.

cond-mat.dis-nn↗

arXiv2014

Degree correlations in signed social networks

We investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are characterized by assortative mixing by degree, networks in which links have a negative connotation, such as disapproval and distrust, are characterized by disassortative patterns. We introduce a class of simple theoretical models to analyze the interplay between network topology and the superimposed structure based on the sign of links. Results uncover the conditions that underpin the emergence of the patterns observed in the data, namely the assortativity of positive subnetworks and the disassortativity of negative ones. We discuss the implications of our study for the analysis of signed complex networks.

physics.soc-ph↗

arXiv2014

Triadic closure as a basic generating mechanism of communities in complex networks

Most of the complex social, technological and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in social networks. Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of community structure, together with fat-tailed distributions of node degree, high clustering coefficients. Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation. Communities are the more pronounced, the sparser the graph, and disappear for high values of link density and randomness in the attachment procedure. By introducing a fitness-based link attractivity for the nodes, we find a novel phase transition, where communities disappear for high heterogeneity of the fitness distribution, but a new mesoscopic organization of the nodes emerges, with groups of nodes being shared between just a few superhubs, which attract most of the links of the system.

physics.soc-ph↗

arXiv2014

Percolation in networks of networks with random matching of nodes in different layers

We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component, generalizing the percolation cluster in a single network to interdependent networks, and observe the strong effect of loops of interdependencies. In particular, we find that the giant mutual component does not emerge in a loop formed by any number of layers. In contrast, we observe multiple hybrid transitions in networks of networks formed by infinite number of randomly connected layers, corresponding to the percolation of layers with different number of interdependencies. In particular we find that layers with many interdependencies are more fragile than layers with less interdependencies. These hybrid transitions, combining a discontinuity and a singularity, are responsible for joining a finite fraction of nodes in different layers to the giant mutually connected component. In the case of partial interdependence, when only a fraction of interlinks between layers provide interdependence, some of these transitions can become continuous.

cond-mat.dis-nn↗

arXiv2014

Critical behavior at the dynamic Mott transition

We investigate magnetoresistance of a square array of superconducting islands placed on a normal metal, which offers a unique tunable laboratory for realizing and exploring quantum many-body systems and their dynamics. A vortex Mott insulator where magnetic field-induced vortices are frozen in the dimples of the egg crate potential by their strong repulsion interaction is discovered. We find an insulator-to-metal transition driven by the applied electric current and determine critical exponents that exhibit striking similarity with the common thermodynamic liquid-gas transition. A simple and straightforward quantum mechanical picture is proposed that describes both tunneling dynamics in the deep insulating state and the observed scaling behavior in the vicinity of the critical point. Our findings offer a comprehensive description of dynamic Mott critical behavior and establish a deep connection between equilibrium and nonequilibrium phase transitions.

cond-mat.supr-con↗

arXiv2014

Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes

The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the network to the desired dynamical state if an external signal is applied to them. Using the framework of structural controllability, here we show that the density of nodes with in-degree and out-degree equal to $0$, $1$ and $2$ determines the number of driver nodes of random networks. Moreover we show that networks with minimum in-degree and out-degree greater than 2, are always fully controllable by an infinitesimal fraction of driver nodes, regardless on the other properties of the degree distribution. Finally, based on these results, we propose an algorithm to improve the controllability of networks.

cond-mat.stat-mech↗

arXiv2014

Non-linear growth and condensation in multiplex networks

Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which one node in each layer attracts an extensive fraction of all the edges.

physics.soc-ph↗

arXiv2014

Multiple percolation transitions in a configuration model of network of networks

Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually connected component when a fraction of nodes have been removed from these networks. Here we characterize the emergence of the mutually connected component in a network of networks in which every node of a network (layer) $α$ is connected with $q_α$ randomly chosen replicas in some other networks and is interdependent of these nodes with probability $r$. We find that when the superdegrees $q_α$ of different layers in the network of networks are distributed heterogeneously, multiple percolation phase transition can occur, and depending on the value of $r$ these transition are continuous or discontinuous.

cond-mat.stat-mech↗

arXiv2014

Entropy distribution and condensation in random networks with a given degree distribution

The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets with respect to a random hypothesis. In many real networks the degrees of individual nodes are not fixed but change in time, while their statistical properties, such as the degree distribution, are preserved. Here we characterize the distribution of entropy of random networks with given degree sequences, where each degree sequence is drawn randomly from a given degree distribution. We show that the leading term of the entropy of scale-free network ensembles depends only on the network size and average degree, and that entropy is self-averaging, meaning that its relative variance vanishes in the thermodynamic limit. We also characterize large fluctuations of entropy that are fully determined by the average degree in the network. Finally, above a certain threshold, large fluctuations of the average degree in the ensemble can lead to condensation, meaning that a single node in a network of size~$N$ can attract $O(N)$ links.

cond-mat.dis-nn↗

arXiv2014

Condensation and topological phase transitions in a dynamical network model with rewiring of the links

Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities are modulated by the negative fitness of the nodes and by the constraint for the network to be a simple graph. At low temperatures and high rewiring rates, this constraint induces a Bose-Einstein condensation of paths of length 2, i.e. a new phase transition with an extended condensate of links. The phase space of the model includes further transitions in the scaling of the connected component and the degeneracy of the network.

cond-mat.dis-nn↗

arXiv2013

Percolation in Multiplex Networks with Overlap

From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers). Multiplexes may display an increased fragility with respect to the single layers that constitute them. However, so far the overlap of the links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. Here we show that the overlap among layers can improve the robustness of interdependent multiplex systems and change the critical behavior of the percolation phase transition in a complex way.

cond-mat.stat-mech↗

arXiv2013

Weighted Multiplex Networks

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multiparticipation ratio. Finally, we introduce a theoretical framework based on the entropy of multiplex ensembles to quantify the information stored in multiplex networks that would remain undetected if the single layers were analyzed in isolation.

physics.soc-ph↗