arXiv subjects

Albert-Laszlo Barabasi

Publications and source records attributed to Albert-Laszlo Barabasi.

At least 37 records · Page 2Linked to original sources

arXiv2007

Quantifying social group evolution

The rich set of interactions between individuals in the society results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimisation of the society as a whole. We have developed a new algorithm based on clique percolation, that allows, for the first time, to investigate the time dependence of overlapping communities on a large scale and as such, to uncover basic relationships characterising community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist longer if they are capable of dynamically altering their membership, suggesting that an ability to change the composition results in better adaptability. The behaviour of small groups displays the opposite tendency, the condition for stability being that their composition remains unchanged. We also show that the knowledge of the time commitment of the members to a given community can be used for estimating the community's lifetime. These findings offer a new view on the fundamental differences between the dynamics of small groups and large institutions.

stat.ME↗

arXiv2007

Analysis of a large-scale weighted network of one-to-one human communication

We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities. We give an account of motif intensity and coherence distributions and compare them to a randomized reference system. We also use the concept of link overlap to measure the number of common neighbors any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing strong quantitative evidence for the weak ties hypothesis, a central concept in social network analysis. The percolation properties of the network are found to depend on the type and order of removed links, and they can help understand how the local structure of the network manifests itself at the global level. We hope that our results will contribute to modeling weighted large-scale social networks, and believe that the systematic approach followed here can be adopted to study other weighted networks.

physics.soc-ph↗

arXiv2006

Burstiness and Memory in Complex Systems

The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. We introduce two measures to distinguish the mechanisms responsible for the bursty nature of real signals, changes in the interevent times and memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up new avenues for future work.

physics.data-an↗

arXiv2005

The inhomogeneous evolution of subgraphs and cycles in complex networks

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.

cond-mat.dis-nn↗

arXiv2004

Multiscaling and non-universality in fluctuations of driven complex systems

For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored, allowing us to separate each signal into a component attributed to the external driving force and one to the internal dynamics. We propose a formalism to capture the potential multiscaling in the fluctuations and apply it to the high frequency trading records of the New York Stock Exchange. We find that on the time scale of minutes the dynamics is governed by internal processes, while on a daily or longer scale the external factors dominate. This transition from internal to external dynamics induces systematic changes in the scaling exponents, offering direct evidence of non-universality in the system.

cond-mat.stat-mech↗

arXiv2004

Reverse engineering of linking preferences from network restructuring

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.

cond-mat.stat-mech↗

arXiv2003

Bioinformatics analysis of experimentally determined protein complexes in the yeast, S. cerevisiae

Many important cellular functions are implemented by protein complexes that act as sophisticated molecular machines of varying size and temporal stability. Here we demonstrate quantitatively that protein complexes in the yeast, Saccharomyces cerevisiae, are comprised of a core in which subunits are highly coexpressed, display the same deletion phenotype (essential or non-essential) and share identical functional classification and cellular localization. This core is surrounded by a functionally mixed group of proteins, which likely represent short-lived- or spurious attachments. The results allow us to define the deletion phenotype and cellular task of most known complexes, and to identify with high confidence the biochemical role of hundreds of proteins with yet unassigned functionality.

q-bio.MN↗

arXiv2002

Hierarchical Organization in Complex Networks

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the World Wide Web, actor network, the Internet at the domain level and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems.

cond-mat.stat-mech↗

arXiv2002

Halting viruses in scale-free networks

The vanishing epidemic threshold for viruses spreading on scale-free networks indicate that traditional methods, aiming to decrease a virus' spreading rate cannot succeed in eradicating an epidemic. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate a virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus' spreading rate. Furthermore, such biased policies are more cost effective, requiring less cures to eradicate the virus.

cond-mat.stat-mech↗

arXiv2002

Deterministic Scale-Free Networks

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.

cond-mat.stat-mech↗

arXiv2001

Modeling the Internet's Large-Scale Topology

Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining the most extensive data on the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet's router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models, and indicate that the networks created by all available topology generators are significantly different from the Internet.

cond-mat.stat-mech↗

arXiv2001

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.

cond-mat.stat-mech↗

arXiv2001

Lethality and centrality in protein networks

In this paper we present the first mathematical analysis of the protein interaction network found in the yeast, S. cerevisiae. We show that, (a) the identified protein network display a characteristic scale-free topology that demonstrate striking similarity to the inherent organization of metabolic networks in particular, and to that of robust and error-tolerant networks in general. (b) the likelihood that deletion of an individual gene product will prove lethal for the yeast cell clearly correlates with the number of interactions the protein has, meaning that highly-connected proteins are more likely to prove essential than proteins with low number of links to other proteins. These results suggest that a scale-free architecture is a generic property of cellular networks attributable to universal self-organizing principles of robust and error-tolerant networks and that will likely to represent a generic topology for protein-protein interactions.

cond-mat.stat-mech↗

arXiv2001

Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to describe the spectral density of uncorrelated random graphs, much less is known about the eigenvalues 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 than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop new methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random graphs does not converge to the semi-circle law. Furthermore, the spectral densities of real-world graphs have specific features depending on the details of the corresponding models. In particular, scale-free graphs develop a triangle-like spectral density with a power law tail, while small-world graphs have a complex spectral density function consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

cond-mat.stat-mech↗

arXiv2000

Error and attack tolerance of complex networks

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.

cond-mat.dis-nn↗

arXiv2000

Topology of evolving networks: local events and universality

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 the numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors.

cond-mat.dis-nn↗

arXiv1999

Emergence of scaling in random networks

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

cond-mat.dis-nn↗

arXiv1999

The diameter of the world wide web

Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and characterize the Internet's infrastructure, little is known about the topology of the web. Here we take a first step to fill this gap: we use local connectivity measurements to construct a topological model of the world wide web, allowing us to explore and characterize its large scale properties.

cond-mat.dis-nn↗