Open Access. Powered by Scholars. Published by Universities.^{®}

- Publication

- File Type

Articles **1** - **22** of ** 22**

## Full-Text Articles in Physics

Immunization Of Complex Networks, R Pastor-Satorras, A Vespignani

#### Immunization Of Complex Networks, R Pastor-Satorras, A Vespignani

*Alessandro Vespignani*

Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity provides an ideal environment for the spreading of infective agents. Here we show that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. The absence of any critical immunization threshold is due to the unbounded connectivity fluctuations of ...

Epidemic Dynamics And Endemic States In Complex Networks, R Pastor-Satorras, A Vespignani

#### Epidemic Dynamics And Endemic States In Complex Networks, R Pastor-Satorras, A Vespignani

*Alessandro Vespignani*

We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding. computer virus epidemics ...

Velocity And Hierarchical Spread Of Epidemic Outbreaks In Scale-Free Networks, M Barthelemy, A Barrat, R Pastor-Satorras, A Vespignani

#### Velocity And Hierarchical Spread Of Epidemic Outbreaks In Scale-Free Networks, M Barthelemy, A Barrat, R Pastor-Satorras, A Vespignani

*Alessandro Vespignani*

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.

Entropy Measures For Complex Networks: Toward An Information Theory Of Complex Topologies, Kartik Anand, Ginestra Bianconi

#### Entropy Measures For Complex Networks: Toward An Information Theory Of Complex Topologies, Kartik Anand, Ginestra Bianconi

*Ginestra Bianconi*

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.

Human Disease Classification In The Postgenomic Era: A Complex Systems Approach To Human Pathobiology, Joseph Loscalzo, Isaac Kohane, Albert-László Barabási

#### Human Disease Classification In The Postgenomic Era: A Complex Systems Approach To Human Pathobiology, Joseph Loscalzo, Isaac Kohane, Albert-László Barabási

*Albert-László Barabási*

Contemporary classification of human disease derives from observational correlation between pathological analysis and clinical syndromes. Characterizing disease in this way established a nosology that has served clinicians well to the current time, and depends on observational skills and simple laboratory tools to define the syndromic phenotype. Yet, this time-honored diagnostic strategy has significant shortcomings that reflect both a lack of sensitivity in identifying preclinical disease, and a lack of specificity in defining disease unequivocally. In this paper, we focus on the latter limitation, viewing it as a reflection both of the different clinical presentations of many diseases (variable phenotypic expression ...

Spectra Of "Real-World" Graphs: Beyond The Semicircle Law, Illés J. Farkas, Imre Derényi, Albert-László Barabási, Tamás Vicsek

#### Spectra Of "Real-World" Graphs: Beyond The Semicircle Law, Illés J. Farkas, Imre Derényi, Albert-László Barabási, Tamás Vicsek

*Albert-László Barabási*

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more ...

Separating The Internal And External Dynamics Of Complex Systems, M. Argollo De Menezes, A.-L. Barabási

#### Separating The Internal And External Dynamics Of Complex Systems, M. Argollo De Menezes, A.-L. Barabási

*Albert-László Barabási*

The observable behavior of a complex system reflects the mechanisms governing the internal interactions between the system’s components and the effect of external perturbations. Here we show that by capturing the simultaneous activity of several of the system’s components we can separate the internal dynamics from the external fluctuations. The method allows us to systematically determine the origin of fluctuations in various real systems, finding that while the Internet and the computer chip have robust internal dynamics, highway and Web traffic are driven by external demand. As multichannel measurements are becoming the norm in most fields, the method ...

Dynamics Of Information Access On The Web, Z. Dezsö, E. Almaas, A. Lukács, B. Rácz, I. Szakadát, A.-L. Barabási

#### Dynamics Of Information Access On The Web, Z. Dezsö, E. Almaas, A. Lukács, B. Rácz, I. Szakadát, A.-L. Barabási

*Albert-László Barabási*

While current studies on complex networks focus on systems that change relatively slowly in time, the structure of the most visited regions of the web is altered at the time scale from hours to days. Here we investigate the dynamics of visitation of a major news portal, representing the prototype for such a rapidly evolving network. The nodes of the network can be classified into stable nodes, which form the timeindependent skeleton of the portal, and news documents. The visitations of the two node classes are markedly different, the skeleton acquiring visits at a constant rate, while a news document ...

Topology Of Evolving Networks: Local Events And Universality, Réka Albert, Albert-László Barabási

#### Topology Of Evolving Networks: Local Events And Universality, Réka Albert, Albert-László Barabási

*Albert-László Barabási*

Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can emerge, the connectivity distribution following either a generalized power law or an exponential. We propose a continuum theory that predicts these two regimes as well as the scaling function and the exponents, in good agreement with numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors.

Weighted Evolving Networks, S. Yook, H. Jeong, A.-L. Barabási, Y. Tu

#### Weighted Evolving Networks, S. Yook, H. Jeong, A.-L. Barabási, Y. Tu

*Albert-László Barabási*

Many biological, ecological, and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most evolving network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total weight distribution converges to the scaling behavior of the connectivity distribution, but this convergence is hampered by strong logarithmic corrections.

Fluctuations In Network Dynamics, M. De Menezes, A.-L. Barabási

#### Fluctuations In Network Dynamics, M. De Menezes, A.-L. Barabási

*Albert-László Barabási*

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the system’s internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.

Critical Fluctuations In Spatial Complex Networks, Serena Bradde, Fabio Caccioli, Luca Dall'asta, Ginestra Bianconi

#### Critical Fluctuations In Spatial Complex Networks, Serena Bradde, Fabio Caccioli, Luca Dall'asta, Ginestra Bianconi

*Ginestra Bianconi*

An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a break-down of this scenario can be obtained when complex networks are embedded in geometrical spaces. Through the analysis of the Ising model on annealed spatial networks, we reveal in particular the spectral properties of networks responsible for critical fluctuations and we generalize the Ginsburg criterion to complex topologies.

Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási

#### Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási

*Ginestra Bianconi*

The evolution of many complex systems, including the World Wide Web, business, and citation networks, is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and nonequilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the "first-mover-advantage," "fit-get-rich," and "winner-takes-all" phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.

Spectra Of "Real-World" Graphs: Beyond The Semicircle Law, Illés J. Farkas, Imre Derényi, Albert-László Barabási, Tamás Vicsek

*Albert-László Barabási*

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more ...

Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási

#### Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási

*Albert-László Barabási*

The evolution of many complex systems, including the World Wide Web, business, and citation networks, is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and nonequilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the "first-mover-advantage," "fit-get-rich," and "winner-takes-all" phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.

Topology Of Evolving Networks: Local Events And Universality, Réka Albert, Albert-László Barabási

#### Topology Of Evolving Networks: Local Events And Universality, Réka Albert, Albert-László Barabási

*Albert-László Barabási*

Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can emerge, the connectivity distribution following either a generalized power law or an exponential. We propose a continuum theory that predicts these two regimes as well as the scaling function and the exponents, in good agreement with numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors.

Impact Of Non-Poissonian Activity Patterns On Spreading Processes, Alexei Vazquez, Balázs Rácz, András Lukács, Albert-László Barabási

#### Impact Of Non-Poissonian Activity Patterns On Spreading Processes, Alexei Vazquez, Balázs Rácz, András Lukács, Albert-László Barabási

*Albert-László Barabási*

Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicates that the intercontact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer ...

Inhomogeneous Evolution Of Subgraphs And Cycles In Complex Networks, Alexei Vázquez, J. G. Oliveira, Albert-László Barabási

#### Inhomogeneous Evolution Of Subgraphs And Cycles In Complex Networks, Alexei Vázquez, J. G. Oliveira, Albert-László Barabási

*Albert-László Barabási*

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network’s degree distribution and clustering properties. This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.

The Architecture Of Complexity, Albert-László Barabási

#### The Architecture Of Complexity, Albert-László Barabási

*Albert-László Barabási*

No abstract provided.

Human Disease Classification In The Postgenomic Era: A Complex Systems Approach To Human Pathobiology, Joseph Loscalzo, Isaac Kohane, Albert-László Barabási

*Albert-László Barabási*

Contemporary classification of human disease derives from observational correlation between pathological analysis and clinical syndromes. Characterizing disease in this way established a nosology that has served clinicians well to the current time, and depends on observational skills and simple laboratory tools to define the syndromic phenotype. Yet, this time-honored diagnostic strategy has significant shortcomings that reflect both a lack of sensitivity in identifying preclinical disease, and a lack of specificity in defining disease unequivocally. In this paper, we focus on the latter limitation, viewing it as a reflection both of the different clinical presentations of many diseases (variable phenotypic expression ...

Predicting Synthetic Rescues In Metabolic Networks, Adilson E. Motter, Natali Gulbahce, Eivind Almaas, Albert-László Barabási

#### Predicting Synthetic Rescues In Metabolic Networks, Adilson E. Motter, Natali Gulbahce, Eivind Almaas, Albert-László Barabási

*Albert-László Barabási*

An important goal of medical research is to develop methods to recover the loss of cellular function due to mutations and other defects. Many approaches based on gene therapy aim to repair the defective gene or to insert genes with compensatory function. Here, we propose an alternative, network-based strategy that aims to restore biological function by forcing the cell to either bypass the functions affected by the defective gene, or to compensate for the lost function. Focusing on the metabolism of single-cell organisms, we computationally study mutants that lack an essential enzyme, and thus are unable to grow or have ...

Multirelational Organization Of Large-Scale Social Networks In An Online World, Renaud Lambiotte

#### Multirelational Organization Of Large-Scale Social Networks In An Online World, Renaud Lambiotte

*Renaud Lambiotte*

The capacity to collect fingerprints of individuals in online media has revolutionized the way researchers explore human society. Social systems can be seen as a nonlinear superposition of a multitude of complex social networks, where nodes represent individuals and links capture a variety of different social relations. Much emphasis has been put on the network topology of social interactions, however, the multidimensional nature of these interactions has largely been ignored, mostly because of lack of data. Here, for the first time, we analyze a complete, multirelational, large social network of a society consisting of the 300,000 odd players of ...