arXiv subjects

Ginestra Bianconi

Publications and source records attributed to Ginestra Bianconi.

At least 109 records · Page 6Linked to original sources

arXiv2017

Weighted Growing Simplicial Complexes

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial complexes are weighted. Here we propose a non-equilibrium model for weighted growing simplicial complexes. The proposed dynamics is able to generate weighted simplicial complexes with a rich interplay between weights and topology emerging not just at the level of nodes and links, but also at the level of faces of higher dimension.

physics.soc-ph↗

arXiv2017

Epidemic spreading and bond percolation in multilayer networks

The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the analytical expression for the epidemic threshold and the fraction of the infected individuals in arbitrary number of layers. These results provide an exact prediction of the epidemic threshold for infinite locally tree-like multilayer networks, and an lower bound of the epidemic threshold for more general multilayer networks. The case of a multilayer network formed by two interconnected networks is specifically studied as a function of the degree distribution within and across the layers. We show that the epidemic threshold strongly depends on the degree correlations of the multilayer structure. Finally we relate our results to the results obtained in the annealed approximation for the Susceptible-Infected-Susceptible (SIS) model.

q-bio.PE↗

arXiv2016

Emergent Hyperbolic Network Geometry

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.

physics.soc-ph↗

arXiv2016

Functional Multiplex PageRank

Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having different connotations forming the different layers of the multiplex. Characterizing the centrality of the nodes in a multiplex network is a challenging task since the centrality of the node naturally depends on the importance associated to links of a certain type. Here we propose to assign to each node of a multiplex network a centrality called Functional Multiplex PageRank that is a function of the weights given to every different pattern of connections (multilinks) existent in the multiplex network between any two nodes. Since multilinks distinguish all the possible ways in which the links in different layers can overlap, the Functional Multiplex PageRank can describe important non-linear effects when large relevance or small relevance is assigned to multilinks with overlap. Here we apply the Functional Page Rank to the multiplex airport networks, to the neuronal network of the nematode c.elegans, and to social collaboration and citation networks between scientists. This analysis reveals important differences existing between the most central nodes of these networks, and the correlations between their so called "pattern to success".

physics.soc-ph↗

arXiv2016

Percolation in real multiplex networks

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where nodes are present in the system with given probability. The approach relies on the locally treelike ansatz, so that it is expected to accurately reproduce the true percolation diagram of sparse multiplex networks with negligible number of short loops. The performance of our theory is tested in social, biological, and transportation multiplex graphs. When compared against previously introduced methods, we observe improvements in the prediction of the percolation diagrams in all networks analyzed. Results from our method confirm previous claims about the robustness of real multiplex networks, in the sense that the average connectedness of the system does not exhibit any significant abrupt change as its individual components are randomly destroyed.

physics.soc-ph↗

arXiv2016

Message passing theory for percolation models on multiplex networks with link overlap

Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers $M$. Specifically we propose and compare two message passing algorithms, that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has non-trivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

physics.soc-ph↗

arXiv2016

Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration networks. Here we characterize the structure of simplicial complexes using their generalized degrees that capture fundamental properties of one, two, three or more linked nodes. Moreover we introduce the configuration model and the canonical ensemble of simplicial complexes, enforcing respectively the sequence of generalized degrees of the nodes and the sequence of the expected generalized degrees of the nodes. We evaluate the entropy of these ensembles, finding the asymptotic expression for the number of simplicial complexes in the configuration model. We provide the algorithms for the construction of simplicial complexes belonging to the configuration model and the canonical ensemble of simplicial complexes. We give an expression for the structural cutoff of simplicial complexes that for simplicial complexes of dimension $d=1$ reduces to the structural cutoff of simple networks. Finally we provide a numerical analysis of the natural correlations emerging in the configuration model of simplicial complexes without structural cutoff.

physics.soc-ph↗

arXiv2016

Extracting Information from Multiplex Networks

Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference problems defined on multiplex networks are fundamental questions of network science. In this paper we discuss the relevance of the Multiplex PageRank algorithm for measuring the centrality of nodes in multilayer networks and we characterize the utility of the recently introduced indicator function $\widetildeΘ^{S}$ for describing their mesoscale organization and community structure. As working examples for studying these measures we consider three multiplex network datasets coming for social science.

physics.soc-ph↗

arXiv2016

Correlated Edge Overlaps in Multiplex Networks

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and non-overlapping links markedly change the phase diagram of the system, leading to multiple hybrid phase transitions. For assortative correlations we observe recurrent hybrid phase transitions.

physics.soc-ph↗

arXiv2016

Multiplex networks with heterogeneous activities of the nodes

In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes and we study their robustness properties. We introduce a percolation model where nodes need to belong to the giant component only on the layers where they are active (i.e. their degree on that layer is larger than zero). We show that when there are enough nodes active only in one layer, the multiplex becomes more resilient and the transition becomes continuous. We find that multiplex networks with a power-law distribution of node activities are more fragile if the distribution of activity is broader. We also show that while positive correlations between node activity and degree can enhance the robustness of the system, the phase transition may become discontinuous, making the system highly unpredictable.

physics.soc-ph↗

arXiv2016

Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity Similarity Optimization (PSO) model represents - at the moment - the climax of this theory. It suggests that the trade-off between node popularity and similarity is a mechanism to explain how complex network topologies emerge - as discrete samples - from the continuous world of hyperbolic geometry. The hyperbolic space seems appropriate to represent real complex networks. In fact, it preserves many of their fundamental topological properties, and can be exploited for real applications such as, among others, link prediction and community detection. Here, we observe for the first time that a topological-based machine learning class of algorithms - for nonlinear unsupervised dimensionality reduction - can directly approximate the network's node angular coordinates of the hyperbolic model into a two-dimensional space, according to a similar topological organization that we named angular coalescence. On the basis of this phenomenon, we propose a new class of algorithms that offers fast and accurate coalescent embedding of networks in the hyperbolic space even for graphs with thousands of nodes.

cond-mat.dis-nn↗

arXiv2016

Network geometry with flavor: from complexity to quantum geometry

Here we introduce the Network Geometry with Flavor $s=-1,0,1$ (NGF) describing simplicial complexes defined in arbitrary dimension $d$ and evolving by a non-equilibrium dynamics. The NGF can generate discrete geometries of different nature, ranging from chains and higher dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution and non-trivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási model for complex networks the stochastic Apollonian network, and the recently introduced model for Complex Quantum Network Manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality $d$. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states are evolving by a Markovian dynamics and a quantum network state at time $t$ encodes all possible NGF evolutions up to time $t$. Interestingly the NGF remains fully classical but its statistical properties reveal the relation to its quantum mechanical description. In fact the $δ$-dimensional faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann or Bose-Einstein statistics depending on the flavor $s$ and the dimensions $d$ and $δ$.

cond-mat.stat-mech↗

arXiv2016

Emergence of multiplex communities in collaboration networks

Community structures in collaboration networks reflect the natural tendency of individuals to organize their work in groups in order to better achieve common goals. In most of the cases, individuals exploit their connections to introduce themselves to new areas of interests, giving rise to multifaceted collaborations which span different fields. In this paper, we analyse collaborations in science and among movie actors as multiplex networks, where the layers represent respectively research topics and movie genres, and we show that communities indeed coexist and overlap at the different layers of such systems. We then propose a model to grow multiplex networks based on two mechanisms of intra and inter-layer triadic closure which mimic the real processes by which collaborations evolve. We show that our model is able to explain the multiplex community structure observed empirically, and we infer the strength of the two underlying social mechanisms from real-world systems. Being also able to correctly reproduce the values of intra-layer and inter-layer assortativity correlations, the model contributes to a better understanding of the principles driving the evolution of social networks.

physics.soc-ph↗

arXiv2016

Control of Multilayer Networks

The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast majority of complex systems are formed by multilayer networks. Here we build a theoretical framework for the linear controllability of multilayer networks by mapping the problem into a combinatorial matching problem. We found that correlating the external signals in the different layers can significantly reduce the multiplex network robustness to node removal, as it can be seen in conjunction with a hybrid phase transition occurring in interacting Poisson networks. Moreover we observe that multilayer networks can stabilize the fully controllable multiplex network configuration that can be stable also when the full controllability of the single network is not stable.

physics.soc-ph↗

arXiv2015

Mesoscopic Structures Reveal the Network Between the Layers of Multiplex Datasets

Multiplex networks describe a large variety of complex systems, whose elements (nodes) can be connected by different types of interactions forming different layers (networks) of the multiplex. Multiplex networks include social networks, transportation networks or biological networks in the cell or in the brain. Extracting relevant information from these networks is of crucial importance for solving challenging inference problems and for characterizing the multiplex networks microscopic and mesoscopic structure. Here we propose an information theory method to extract the network between the layers of multiplex datasets, forming a "network of networks". We build an indicator function, based on the entropy of network ensembles, to characterize the mesoscopic similarities between the layers of a multiplex network and we use clustering techniques to characterize the communities present in this network of networks. We apply the proposed method to study the Multiplex Collaboration Network formed by scientists collaborating on different subjects and publishing in the Americal Physical Society (APS) journals. The analysis of this dataset reveals the interplay between the collaboration networks and the organization of knowledge in physics.

physics.soc-ph↗

arXiv2015

Interdisciplinary and physics challenges of Network Theory

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.

physics.soc-ph↗

arXiv2015

Complex Quantum Network Geometries: Evolution and Phase Transitions

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e. simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a non-equilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped respectively to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks including small-world property, high clustering coefficient, high modularity, scale-free degree distribution.Moreover they can be distinguished between the Fermi-Dirac Network and the Bose-Einstein Network obeying respectively the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally we comment on the relation between Quantum Complex Network Geometries, spin networks and triangulations.

cond-mat.dis-nn↗

arXiv2015

Complex Quantum Network Manifolds in Dimension $d>2$ are Scale-Free

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension $d$. We show that in $d=2$ CQNM are homogeneous networks while for $d>2$ they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the $δ$-faces of the $d$-dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the $δ$-faces.

gr-qc↗