arXiv subjects

Tamas Vicsek

Publications and source records attributed to Tamas Vicsek.

At least 37 records · Page 2Linked to original sources

arXiv2008

Fundamental statistical features and self-similar properties of tagged networks

We investigate the fundamental statistical features of tagged (or annotated) networks having a rich variety of attributes associated with their nodes. Tags (attributes, annotations, properties, features, etc.) provide essential information about the entity represented by a given node, thus, taking them into account represents a significant step towards a more complete description of the structure of large complex systems. Our main goal here is to uncover the relations between the statistical properties of the node tags and those of the graph topology. In order to better characterise the networks with tagged nodes, we introduce a number of new notions, including tag-assortativity (relating link probability to node similarity), and new quantities, such as node uniqueness (measuring how rarely the tags of a node occur in the network) and tag-assortativity exponent. We apply our approach to three large networks representing very different domains of complex systems. A number of the tag related quantities display analogous behaviour (e.g., the networks we studied are tag-assortative, indicating possible universal aspects of tags versus topology), while some other features, such as the distribution of the node uniqueness, show variability from network to network allowing for pin-pointing large scale specific features of real-world complex networks. We also find that for each network the topology and the tag distribution are scale invariant, and this self-similar property of the networks can be well characterised by the tag-assortativity exponent, which is specific to each system.

physics.soc-ph↗

arXiv2008

Centrality properties of directed module members in social networks

Several recent studies of complex networks have suggested algorithms for locating network communities, also called modules or clusters, which are mostly defined as groups of nodes with dense internal connections. Along with the rapid development of these clustering techniques, the ability of revealing overlaps between communities has become very important as well. An efficient search technique for locating overlapping modules is provided by the Clique Percolation Method (CPM) and its extension to directed graphs, the CPMd algorithm. Here we investigate the centrality properties of directed module members in social networks obtained from e-mail exchanges and from sociometric questionnaires. Our results indicate that nodes in the overlaps between modules play a central role in the studied systems. Furthermore, the two different types of networks show interesting differences in the relation between the centrality measures and the role of the nodes in the directed modules.

physics.soc-ph↗

arXiv2008

Turning with the others: novel transitions in an SPP model with coupling of accelerations

We consider a three dimensional, generalized version of the original SPP model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the self-propelled particles (SPP-s) depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We argue that in nature evolutionary processes can drive the strategy variable s towards the critical point, where information exchange between the units of a system is maximal.

cond-mat.stat-mech↗

arXiv2008

Phase transition in the scalar noise model of collective motion in three dimensions

We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case. For small velocity (v <= 0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to a boundary condition dependent symmetry breaking of the solutions.

cond-mat.stat-mech↗

arXiv2007

Directed network modules

A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdos-Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Google's own webpages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and among Google's webpages the overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory networks tend to overlap via out-hubs.

physics.soc-ph↗

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

Weighted network modules

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdos-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.

cond-mat.stat-mech↗

arXiv2006

Collective behavior of interacting self-propelled particles

We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the results of large scale simulations and theoretical approaches to the problem.

cond-mat.stat-mech↗

arXiv2006

Spontaneously ordered motion of self-propelled particles

We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbors by choosing at each time step a velocity direction equal to the average direction of their neighbors. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte-Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow $ϕ$ emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise $η$ and the average density of the particles $\varrho$ is calculated and is found to have the form $η_c(\varrho)\sim \varrho^{1/2}$. We also find that $ϕ$ scales as a function of the external bias $h$ (field or ``wind'') according to a power law $ϕ\sim h^{0.9}$. In the ordered phase the system shows long-range correlated fluctuations and $1/f$ noise.

cond-mat.stat-mech↗

arXiv2006

Novel type of phase transition in a system of self-driven particles

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation ($η$) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $| {\bf v}_a | =0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since $| {\bf v}_a |$ is found to scale as $(η_c-η)^β$ with $β\simeq 0.45$.

cond-mat.stat-mech↗

arXiv2006

New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder-order transition in the SNM is a continuous, second order phase transition for small particle velocities ($v\leq 0.1$). However, for large velocities ($v\geq 0.3$) we find a strong anisotropy in the particle diffusion in contrast with the isotropic diffusion for small velocities. The interplay between the anisotropic diffusion and the periodic boundary conditions leads to an artificial symmetry breaking of the solutions (directionally quantized density waves) and a consequent first order transition like behavior. Thus, it is not possible to draw any conclusion about the physical behavior in the large particle velocity regime of the SNM.

nlin.AO↗

arXiv2006

Phase transition in the collective migration of tissue cells: experiment and model

We have recorded the swarming-like collective migration of a large number of keratocytes (tissue cells obtained from the scales of goldfish) using long-term videomicroscopy. By increasing the overall density of the migrating cells, we have been able to demonstrate experimentally a kinetic phase transition from a disordered into an ordered state. Near the critical density a complex picture emerges with interacting clusters of cells moving in groups. Motivated by these experiments we have constructed a flocking model that exhibits a continuous transition to the ordered phase, while assuming only short-range interactions and no explicit information about the knowledge of the directions of motion of neighbors. Placing cells in microfabricated arenas we found spectacular whirling behavior which we could also reproduce in simulations.

q-bio.CB↗

arXiv2006

The critical point of k-clique percolation in the Erdos-Renyi graph

Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes being connected is above a certain threshold p_c(k), the complete subgraphs of size k (the k-cliques) are organized into a giant cluster. By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism. From the divergence of this average size we then derive an analytic expression for the critical linking probability p_c(k).

cond-mat.dis-nn↗

arXiv2006

CFinder: Locating cliques and overlapping modules in biological networks

Summary: Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein assocation network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the modules (overlaps). We introduce CFinder, a fast program locating and visualizing overlapping, densely interconnected groups of nodes in undirected graphs, and allowing the user to easily navigate between the original graph and the web of these groups. We show that in gene (protein) association networks CFinder can be used to predict the function(s) of a single protein and to discover novel modules. CFinder is also very efficient for locating the cliques of large sparse graphs. Availability: CFinder (for Windows, Linux, and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering. Contact: cfinder@angel.elte.hu

q-bio.MN↗

arXiv2006

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.

cond-mat.stat-mech↗

arXiv2006

Initiating a Mexican wave: An instantaneous collective decision with both short and long range interactions

An interesting example for collective decision making is the so-called Mexican wave during which the spectators in a stadium leap to their feet with their arms up and then sit down again following those to their left (right) with a small delay. Here we use a simple, but realistic model to explain how the combination of the local and global interactions of the spectators produces a breaking of the symmetry resulting in the replacement of the symmetric solution -- containing two propagating waves -- by a single wave moving in one of the two possible directions. Our model is based on and compared to the extensive observations of volunteers filling out the related questionnaire we have posted on the Internet. We find that, as a function of the parameter controlling the strength of the global interactions, the transition to the single wave solution has features reminiscent of discontinuous transitions. After the spontaneous symmetry breaking the two directions of propagation are still statistically equivalent. We investigate also how this remaining symmetry is broken in real stadia by a small asymmetrical term in the perception of spectators.

physics.soc-ph↗

arXiv2005

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

physics.soc-ph↗

arXiv2005

Clique percolation in random networks

The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Renyi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold pc(k)=[(k-1)N]^{-1/(k-1)}. At the transition point the scaling of the giant component with N is highly non-trivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.

cond-mat.dis-nn↗