stochastic and mixed flower graphs stochasticity is introduced to a well studied class of recursively grown graphs u v flower nets which have power law degree distributions as well as small world properties when u 1 the stochastic variant interpolates between different deterministic flower graphs thus adding flexibility to the model the random multiplicative growth process involved however leads to a spread ensemble of networks with finite variance for the number of links nodes and loops nevertheless the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs we also study a class of mixed flower networks closely related to the stochastic flowers but which are grown recursively in a deterministic way the deterministic growth of mixed flower nets eliminates ensemble spreads and their recursive growth allows for exact analysis of their uniquely defined mixed properties

a parallel space saving algorithm for frequent items and the hurwitz zeta distribution we design a parallel algorithm for frequent items based on the sequential space saving algorithm we show that the algorithm is cost optimal for k o 1 and therefore extremely fast and useful in a wide range of applications we experimentally validate the algorithm on synthetic data distributed using a hurwitz zeta function and a zipf one and also on real datasets confirming the theoretical cost optimality and that the error committed is very low and close to zero we compare the performances and the error committed by our algorithm against a parallel algorithm recently proposed by agarwal et al for merging datasets derived by the space saving or frequent algorithms we present a message passing based parallel version of the space saving algorithm designed to solve the k majority problem the algorithm determines in parallel frequent items i e those whose frequency is greater than a given threshold and is therefore useful for iceberg queries and many other different contexts we apply our algorithm to the detection of frequent items in both real and synthetic datasets whose probability distribution functions are a hurwitz and a zipf distribution respectively also we compare its parallel performances and accuracy against a parallel algorithm recently proposed for merging summaries derived by the space saving or frequent algorithms

random geometric graphs we analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present the critical connectivity is found numerically by examining the size of the largest cluster we derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs even for infinite dimensionality insights relevant for graph bipartitioning are included

improvement of the robustness on geographical networks by adding shortcuts abstract in a topological structure affected by geographical constraints on liking the connectivity is weakened by constructing local stubs with small cycles a something of randomness to bridge them is crucial for the robust network design in this paper we numerically investigate the effects of adding shortcuts on the robustness in geographical scale free network models under a similar degree distribution to the original one we show that a small fraction of shortcuts is highly contribute to improve the tolerance of connectivity especially for the intentional attacks on hubs the improvement is equivalent to the effect by fully rewirings without geographical constraints on linking even in the realistic internet topologies these effects are virtually examined

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

exact solution of site and bond percolation on small world networks we study percolation on small world networks which has been proposed as a simple model of the propagation of disease the occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively we give an exact solution of the model for both site and bond percolation including the position of the percolation transition at which epidemic behavior sets in the values of the critical exponents governing this transition the mean and variance of the distribution of cluster sizes disease outbreaks below the transition and the size of the giant component epidemic above the transition

constrained markovian dynamics of random graphs we introduce a statistical mechanics formalism for the study of constrained graph evolution as a markovian stochastic process in analogy with that available for spin systems deriving its basic properties and highlighting the role of the mobility the number of allowed moves for any given graph as an application of the general theory we analyze the properties of degree preserving markov chains based on elementary edge switchings we give an exact yet simple formula for the mobility in terms of the graph s adjacency matrix and its spectrum this formula allows us to define acceptance probabilities for edge switchings such that the markov chains become controlled glauber type detailed balance processes designed to evolve to any required invariant measure representing the asymptotic frequencies with which the allowed graphs are visited during the process as a corollary we also derive a condition in terms of simple degree statistics sufficient to guarantee that in the limit where the number of nodes diverges even for state independent acceptance probabilities of proposed moves the invariant measure of the process will be uniform we test our theory on synthetic graphs and on realistic larger graphs as studied in cellular biology showing explicitly that for instances where the simple edge swap dynamics fails to converge to the uniform measure a suitably modified markov chain instead generates the correct phase space sampling

organization of modular networks we examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts char22 communities or modules we develop an analytical approach allowing us to obtain the statistics of connected components and the intervertex distance distribution in these modular networks and to describe their global organization and structure in particular we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks we demonstrate that even a relatively small number of shortcuts unite the networks into one in more precise terms if the number of interlinks is any finite fraction of the total number of connections then the intervertex distance distribution approaches a ensuremath delta function peaked form and so the network is united

asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks we propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model the model we introduce is a variation of the zhang model we investigate the time asymptotic behavior of the corresponding dynamical system in particular the conditions for the existence of an invariant compact asymptotic set and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with poisson connectivity distribution

spinning gas clouds with precession non degenerate cases we extend here our earlier treatment gaffet b 2003 j phys a math gen 36 5211 gaffet b 2005 phil trans r soc a accepted of the evolution of spinning gas clouds with precession to the non degenerate cases where the last integral of motion l6 is non vanishing the liouville torus is still found to be transformable into a quartic surface on which there are 15 conic point singularities the differential system governing the evolution is integrable by quadratures there is an integrating factor and the independent variable u which is the thermasy of the cloud admits an exact differential formulation on the liouville torus as well this integrable system is conjectured to have the painleve property with respect to the independent variable u as in the degenerate cases

percolation in directed scale free networks many complex networks in nature have directed links a property that affects the network s navigability and large scale topology here we study the percolation properties of such directed scale free networks with correlated in and out degree distributions we derive a phase diagram that indicates the existence of three regimes determined by the values of the degree exponents in the first regime we regain the known directed percolation mean field exponents in contrast the second and third regimes are characterized by anomalous exponents which we calculate analytically in the third regime the network is resilient to random dilution i e the percolation threshold is pc 1

enhancing the convergence efficiency of a self propelled agent system via a weighted model we investigate a weighted self propelled agent system wherein each agent s direction is determined by its spatial neighbors directions with exponential weights according to the neighbor numbers in order to describe the fact that some agents with more neighbors might have larger influence on its neighbors we introduce a scaling exponent of the neighbor number between 0 and ensuremath infty when the exponent is equal to 1 the convergence efficiency is enhanced in our simulation furthermore as the exponent increases i e the effect of weight becomes stronger the network of agents becomes easier to achieve direction consensus

bootstrap percolation on complex networks we consider bootstrap percolation on uncorrelated complex networks we obtain the phase diagram for this process with respect to two parameters f the fraction of vertices initially activated and p the fraction of undamaged vertices in the graph we observe two transitions the giant active component appears continuously at a first threshold there may also be a second discontinuous hybrid transition at a higher threshold avalanches of activations increase in size as this second critical point is approached finally diverging at this threshold we describe the existence of a special critical point at which this second transition first appears in networks with degree distributions whose second moment diverges but whose first moment does not we find a qualitatively different behavior in this case the giant active component appears for any fg0 and pg0 and the discontinuous transition is absent this means that the giant active component is robust to damage and also is very easily activated we also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold

promoting collective motion of self propelled agents by discarding short range interactions abstract we study the collective motion of self propelled agents with the restricted view the field of view of each agent is an annulus bounded by the outer radius r and inner radius r where is a tunable parameter we find that there exists an optimal value of leading to the highest degree of direction consensus this phenomenon indicates that there exists superfluous communication in the collective motion of self propelled agents and short range interactions hinder the direction consensus of the system the value of optimal decreases as the absolute velocity increases while it increases as the outer radius r and the system size increase for a fixed value of direction consensus is enhanced when the absolute velocity is small the outer radius or the system size is large

the minimum spanning tree an unbiased method for brain network analysis the brain is increasingly studied with graph theoretical approaches which can be used to characterize network topology however studies on brain networks have reported contradictory findings and do not easily converge to a clear concept of the structural and functional network organization of the brain it has recently been suggested that the minimum spanning tree mst may help to increase comparability between studies the mst is an acyclic sub network that connects all nodes and may solve several methodological limitations of previous work such as sensitivity to alterations in connection strength for weighted networks or link density for unweighted networks which may occur concomitantly with alterations in network topology under empirical conditions if analysis of msts avoids these methodological limitations understanding the relationship between mst characteristics and conventional network measures is crucial for interpreting mst brain network studies here we firstly demonstrated that the mst is insensitive to alterations in connection strength or link density we then explored the behavior of mst and conventional network characteristics for simulated regular and scale free networks that were gradually rewired to random networks surprisingly although most connections are discarded during construction of the mst mst characteristics were equally sensitive to alterations in network topology as the conventional graph theoretical measures the mst characteristics diameter and leaf fraction were very strongly related to changes in the characteristic path length when the network changed from a regular to a random configuration similarly mst degree diameter and leaf fraction were very strongly related to the degree of scale free networks that were rewired to random networks analysis of the mst is especially suitable for the comparison of brain networks as it avoids methodological biases even though the mst does not utilize all the connections in the network it still provides a mathematically defined and unbiased sub network with characteristics that can provide similar information about network topology as conventional graph measures

phenomenological models of socioeconomic network dynamics we study a general set of models of social network evolution and dynamics the models consist of both a dynamics on the network and evolution of the network links are formed preferentially between similar nodes where the similarity is defined by the particular process taking place on the network the interplay between the two processes produces phase transitions and hysteresis as seen using numerical simulations for three specific processes we obtain analytic results using mean field approximations and for a particular case we derive an exact solution for the network in common with real world social networks we find coexistence of high and low connectivity phases and history dependence

insights into bootstrap percolation its equivalence with k core percolation and the giant component k core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems since these models are considerably similar it has been suggested in recent years that they could be complementary in this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k core percolation and vice versa if the functionality thresholds in both processes satisfy a complementary relation another interesting problem in bootstrap and k core percolation is the fraction of nodes belonging to their giant connected components p b and p c respectively we solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions and we show that p b and p c are not complementary our theoretical results coincide with computer simulations in the limit of very large graphs in bootstrap percolation we show that when using the branching theory to compute the size of the giant component we must consider two different types of links which are related to distinct spanning branches of active nodes

a mathematical model for generating bipartite graphs and its application to protein networks complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology most of these systems can be organized into networks composed of nodes and interacting edges here we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes we then use this model to investigate protein domain networks a protein can be composed of up to hundreds of domains each domain represents a conserved sequence segment with specific functional tasks we analyze the distribution of domains in homo sapiens and arabidopsis thaliana organisms and the statistical analysis shows that while a the number of domain types shared by k proteins exhibits a power law distribution b the number of proteins composed of k types of domains decays as an exponential distribution the proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of a power law and b exponential distributions our theoretical and computational results show that this model requires 1 growth process and 2 copy mechanism

localization and centrality in networks eigenvector centrality is a common measure of the importance of nodes in a network here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network in this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired as a remedy we propose an alternative centrality measure based on the nonbacktracking matrix which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails

fractal dimensions of percolating networks we use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in erdos renyi er and random scale free sf networks with degree distribution p k ck we show that the chemical dimension is dl 2 for er and sf networks with 4 as in percolation in d dc 6 dimensions for 3 4 and df 2 2 3 3 4 and dc 2 1 3 3 4 we discuss the meaning of these dimensions for networks

unified index to quantifying heterogeneity of complex networks abstract although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function a unified definition of the heterogeneity of a network with any degree distribution is absent in this paper we define a heterogeneity index 0 h 1 to quantify the degree heterogeneity of any given network we analytically show the existence of an upper bound of h 0 5 for exponential networks thus explain why exponential networks are homogeneous on the other hand we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0 5 if and only if its degree exponent is between 2 and 2 5 we further show that for any power law network with a degree exponent greater than 2 5 there always exists an exponential network such that both networks have the same heterogeneity index this may help to explain why 2 5 is a critical degree exponent for some dynamic behaviors on power law networks

spreading dynamics of forget remember mechanism we study extensively the forget remember mechanism frm for message spreading originally introduced in eur phys j b 62 247 2008 epjbfy1434 602810 1140 epjb e2008 00139 4 the freedom of specifying forget remember functions governing the frm can enrich the spreading dynamics to a very large extent the master equation is derived for describing the frm dynamics by applying the mean field techniques we have shown how the steady states can be reached under certain conditions which agrees well with the monte carlo simulations the distributions of forget and remember times can be explicitly given when the forget remember functions take linear or exponential forms which might shed some light on understanding the temporal nature of diseases like flu for time dependent frm there is an epidemic threshold related to the frm parameters we have proven that the mean field critical transmissibility for the sis model and the critical transmissibility for the sir model are the lower and the the upper bounds of the critical transmissibility for the frm model respectively

random growth urban model with geographical fitness abstract this paper formulates a random growth urban model with a notion of geographical fitness using techniques of complex network theory we study our system as a type of preferential attachment model with fitness and we analyze its macro behavior to clarify the properties of the city size distributions it predicts first restricting the geographical fitness to take positive values and using a continuum approach we show that the city size distributions predicted by our model asymptotically approach pareto distributions with coefficients greater than unity then allowing the geographical fitness to take negative values we perform local coefficient analysis to show that the predicted city size distributions can deviate from pareto distributions as is often observed in actual city size distributions as a result the model we propose can generate a generic class of city size distributions including but not limited to pareto distributions for applications to city population projections our simple model requires randomness only when new cities are created not during their subsequent growth this property leads to smooth trajectories of city population growth in contrast to other models using gibrat s law in addition a discrete form of our dynamical equations can be used to estimate past city populations based on present day data this fact allows quantitative assessment of the performance of our model further study is needed to determine appropriate formulas for the geographical fitness

faber approximation of the mori zwanzig equation abstract we develop new approximations of the mori zwanzig equation based on operator series expansions of the orthogonal dynamics propagator in particular we study the faber polynomial series which yields asymptotically optimal approximations converging at least r superlinearly with the polynomial order numerical applications are presented for random wave propagation and harmonic chains of oscillators interacting on the bethe lattice and on graphs with arbitrary topology most of the analysis and numerical results presented in this paper are for linear dynamical systems evolving from random initial states the extension to nonlinear systems is discussed as well the challenges in the implementation of the proposed approximation methods

self avoiding walks on scale free networks several kinds of walks on complex networks are currently used to analyze search and navigation in different systems many analytical and computational results are known for random walks on such networks self avoiding walks saw s are expected to be more suitable than unrestricted random walks to explore various kinds of real life networks here we study long range properties of random saw s on scale free networks characterized by a degree distribution p k ensuremath sim k ensuremath ensuremath gamma in the limit of large networks system size n ensuremath rightarrow ensuremath infty the average number s n of saw s starting from a generic site increases as ensuremath mu n with ensuremath mu k 2 k ensuremath 1 for finite n s n is reduced due to the presence of loops in the network which causes the emergence of attrition of the paths for kinetic growth walks the average maximum length l increases as a power of the system size l ensuremath sim n ensuremath alpha with an exponent ensuremath alpha increasing as the parameter ensuremath gamma is raised we discuss the dependence of ensuremath alpha on the minimum allowed degree in the network a similar power law dependence is found for the mean self intersection length of nonreversal random walks simulation results support our approximate analytical calculations

a non markovian sir network model with fixed infectious period and preventive rewiring abstract in the face of disease occurrence susceptible individuals tend to protect themselves by rewiring their links i e cutting off connection with infected person and switching to contact with healthy ones therefore the adaptive rewiring mechanism is considered in the network epidemic model moreover the infection periods for different diseases do not always follow exponential distributions in the process of disease transmission which may be of fixed length using the idea of age structure we establish the susceptible infected recovered epidemic model for each node and each link resulting in a delayed non markovian sir pairwise model with fixed infectious period and preventive rewiring then give the pairwise reproduction number r 0 p and provide the formula for the final epidemic size by rigorous analysis and tedious computation the simulation results show that adaptive rewiring inhibits the spread of disease and decreases the size of disease outbreak while the extension of the infectious period promotes disease transmission in addition the numerical simulation results are in good agreement with the stochastic simulation to our best knowledge the approach in building our model is novel the results may provide new insights into the study of the network disease transmission

a directed network of greek and roman mythology abstract we construct a directed network using a dictionary of greek and roman mythology in which the nodes represent the entries listed in the dictionary and we make directional links from an entry to other entries that appear in its explanatory part we find that this network is clearly not a random network but a directed scale free network in which the distributions of out degree and in degree follow a power law with exponents out 3 0 and in 2 5 respectively also we measure several quantities which describe the topological properties of the network and compare it to that of other real networks

general formalism for inhomogeneous random graphs we present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models where vertices come in different types and the probability of realizing an edge depends on the types of its terminal vertices this approach provides a general framework for the analysis of a large class of models the generic phase structure is derived using generating function techniques and relations to other classes of models are pointed out

random sequential renormalization of networks application to critical trees we introduce the concept of random sequential renormalization rsr for arbitrary networks rsr is a graph renormalization procedure that locally aggregates nodes to produce a coarse grained network it is analogous to the quasi parallel renormalization schemes introduced by c song et al c song et al nature london 433 392 2005 and studied by f radicchi et al f radicchi et al phys rev lett 101 148701 2008 but much simpler and easier to implement here we apply rsr to critical trees and derive analytical results consistent with numerical simulations critical trees exhibit three regimes in their evolution under rsr i for n 0 ensuremath nu ensuremath lesssim nl n 0 where n is the number of nodes at some step in the renormalization and n 0 is the initial size of the tree rsr is described by a mean field theory and fluctuations from one realization to another are small the exponent ensuremath nu 1 2 is derived using random walk and other arguments the degree distribution becomes broader under successive steps reaching a power law p k 1 k ensuremath gamma with ensuremath gamma 2 and a variance that diverges as n 0 1 2 at the end of this regime both of these latter results are obtained from a scaling theory ii for n 0 ensuremath nu mathrm star ensuremath lesssim n ensuremath lesssim n 0 1 2 with ensuremath nu mathrm star ensuremath approx 1 4 hubs develop and fluctuations between different realizations of the rsr are large trees are short and fat with an average radius that is mathcal o 1 crossover functions exhibiting finite size scaling in the critical region n n 0 1 2 ensuremath rightarrow ensuremath infty connect the behaviors in the first two regimes iii for n ensuremath lesssim n 0 ensuremath nu mathrm star star configurations appear with a central hub surrounded by many leaves the distribution of stars is broadly distributed over this range the scaling behaviors found under rsr are identified with a continuous transition in a process called agglomerative percolation ap with the coarse grained nodes in rsr corresponding to clusters in ap that grow by simultaneously attaching to all their neighboring clusters

entropy and enumeration of boolean functions shannon s notion of the entropy of a random variable is used to give simplified proofs of asymptotic formulas for the logarithms of the numbers of monotone boolean functions and horn 1951 functions and for equivalent results concerning families of sets and closure operations

consensus in a heterogeneous influence network we consider a dynamical network model in which a number of agents all move on the plane with the same constant absolute velocity at each time step each agent s direction is updated as the average of its direction plus the directions of other agents who can influence it the influencing capability of each agent is represented by its influencing radius which is randomly chosen according to a power law distribution with a scaling exponent between 2 and ensuremath infty as the value of the scaling exponent decreases the radius distribution becomes more heterogeneous and the network becomes much easier to achieve direction consensus among agents due to the leading roles played by a few hub agents furthermore almost all agents will finally move in the same desired direction in a strong heterogeneous influence network if and only if a small fraction of hub agents can be controlled to move in the desired direction these results also reflect the robust yet fragile feature of a heterogeneous influence network

cascading failures on correlated interdependent networks with dependency groups abstract the topologies of interdependent networks markedly affect the cascading failures and phase transition however the effects of interlayer degree correlations on cascading failures on interdependent networks with dependency groups have not been investigated in this paper we propose a cascading failure model on correlated interdependent networks with dependency groups and use a percolation theory to describe the final state of the dynamics through extensive numerical simulations and theoretical analysis we find that interlayer degree correlations enhance the robustness of the system on networks with homogeneous degree distribution the system always exhibits a discontinuous phase transition however on networks with heterogeneous degree distributions the phase transition is continuous discontinuous for strong weak interlayer degree correlations the theoretical and numerical predictions agree well with each other

complex networks in confined comminution the physical process of confined comminution is investigated within the framework of complex networks we first characterize the topology of the unweighted contact networks as generated by the confined comminution process we find this process gives rise to an ultimate contact network which exhibits a scale free degree distribution and small world properties in particular if viewed in the context of networks through which information travels along shortest paths we find that the global average of the node vulnerability decreases as the comminution process continues with individual node vulnerability correlating with grain size a possible application to the design of synthetic networks e g sensor networks is highlighted next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks where each link is weighted by the inverse magnitude of the normal force acting at the associated contact we find that the strong forces i e force chains are transmitted along pathways in the network which are mainly following shortest path routing protocols as typically found for example in communication systems motivated by our earlier studies of the building blocks for self organization in dense granular systems we also explore the properties of the minimal contact cycles the distribution of the contact strain energy intensity of 4 cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale free distribution with infinite variance thereby suggesting that 4 cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking

tailored graph ensembles as proxies or null models for real networks i tools for quantifying structure we study the tailoring of structured random graph ensembles to real networks with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically beyond the level of degree statistics our family of ensembles can produce graphs with any prescribed degree distribution and any degree degree correlation function its control parameters can be calculated fully analytically and as a result we can calculate asymptotically formulae for entropies and complexities and for information theoretic distances between networks expressed directly and explicitly in terms of their measured degree distribution and degree correlations

mean field level analysis of epidemics in directed networks the susceptible infected removed spreading model in a directed graph is studied the mean field level rate equations are built with the degree degree connectivity correlation element and the in out degree distribution and the outbreak threshold is obtained analytically it is determined by the combination of connectivity probability and the degree distribution furthermore the methods of calculating the degree degree correlations in directed networks are presented the numerical results of the discrete epidemic processes in networks verify our analyses

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

class formation in a social network with asset exchange abstract we study two kinds of economic exchanges additive and multiplicative in a system of n agents the work is divided into two parts in the first one the agents are free to interact with each other the system evolves to a boltzmann gibbs distribution with additive exchange and condenses with a multiplicative one if bankruptcy is introduced both types of exchange lead to condensation condensation times have been studied in the second part the agents are placed in a social network we analyze the behavior of wealth distributions in time and the formation of economic classes is observed for certain values of network connectivity

adaptive velocity strategy for swarm aggregation collective behaviors of biological swarms have attracted significant interest in recent years but much attention and efforts have been focused on constant speed models in which all agents are assumed to move with the same constant speed one limitation of the constant speed assumption without attraction function is that global convergence is quite difficult or even practically impossible to achieve if the speed is relatively fast in this paper we propose an adaptive velocity model in which each agent not only adjusts its moving direction but also adjusts its speed according to the degree of direction consensus among its local neighbors one important feature of the adaptive velocity model is that the speeds of all agents are adaptively tuned to the same maximum constant speed after a short transient process the adaptive velocity strategy can greatly enhance the global convergence probability and thus provides a powerful mechanism for coordinated motion in biological and technological multiagent systems

percolation on bipartite scale free networks abstract recent studies introduced biased degree dependent edge percolation as a model for failures in real life systems in this work such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type such bipartite graphs appear in many social networks for instance in affiliation networks and in sexual contact networks in which both types of nodes show the scale free characteristic for the degree distribution during the depreciation process an edge between nodes with degrees k and q is retained with a probability proportional to k q where is positive so that links between hubs are more prone to failure the removal process is studied analytically by introducing a generating functions theory we deduce exact self consistent equations describing the system at a macroscopic level and discuss the percolation transition critical exponents are obtained by exploiting the fortuin kasteleyn construction which provides a link between our model and a limit of the potts model

accelerating consensus of self driven swarm via adaptive speed abstract in recent years the well developed vicsek model has attracted more and more attention unfortunately in depth research on its convergence speed is not yet completed in this paper we investigate some key factors governing the convergence speed of the vicsek model with the assistance of extensive numerical simulations a significant phenomenon surfaces that the convergence time scales obeys a power law with r 2 ln n with r and n being the horizon radius and the number of particles respectively to further accelerate the convergence procedure we propose a kind of improved vicsek model with self driven particles governed by variational speeds which can remarkably shorten the convergence time of the standard vicsek model

spectra of modular and small world matrices we compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter and intra module degree distributions subject only to the constraint of finite mean connectivities we also evaluate spectra of a certain class of small world matrices generated from random graphs by introducing shortcuts via additional random connectivity components both adjacency matrices and the associated graph laplacians are investigated for the laplacians we find lifshitz type singular behaviour of the spectral density in a localized region of small values in the case of modular networks we can identify contributions of local densities of state from individual modules for small world networks we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states exhibiting only localized states in the band gaps results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances and with direct diagonalization results

a special class of painleve differential systems that generalize the elliptic functions a the elliptic functions of order 2 may be viewed as the ratios z2 z1 of the solutions of a differential system of the general form zi3 8d2zj zid u2 zjrii ziriji j i j 1 n where n 2 u is the independent variable and the rij are the homogeneous quadratic functions of the n variables zi the general solution of systems of this form automatically consists for all n of purely meromorphic functions for arbitrary values of n the system consists of n n 1 equations for n 1 inhomogeneous variables zi z1 and the question arises as to whether there may exist systems of the above form with n 2 which are equivalent to a non over determined differential system of p equations when n p 1 appropriately chosen algebraic constraints are imposed on the dependent variables in the present work we show that such systems do exist with n 4 and n 8 and are in fact special cases of the dyson model 1968 of a spinning cloud of ellipsoidal shape expanding adiabatically into a vacuum

counting triangles in massive graphs with mapreduce graphs and networks are used to model interactions in a variety of contexts there is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure some of the most useful metrics are triangle based and give a measure of the connectedness of mutual friends this is often summarized in terms of clustering coefficients which measure the likelihood that two neighbors of a node are themselves connected computing these measures exactly for large scale networks is prohibitively expensive in both memory and time however a recent wedge sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients in this paper we describe how to implement this approach in mapreduce to deal with massive graphs we show results on publicly available networks the largest of which is 132m nodes and 4 7b edges as well as artificially generated networks using the graph500 benchmark the largest of which has 240m nodes and 8 5b edges

spectral methods for community detection and graph partitioning we consider three distinct and well studied problems concerning network structure community detection by modularity maximization community detection by statistical inference and normalized cut graph partitioning each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network we show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are in fact identical and hence that at least within the spectral approximations used here there is no difference between the modularity and inference based community detection methods or between either and graph partitioning

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

reconstructing the world trade multiplex the role of intensive and extensive biases in economic and financial networks the strength of each node has always an important economic meaning such as the size of supply and demand import and export or financial exposure constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown however several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node we study several temporal snapshots and almost 100 layers commodity classes of the multiplex and find that the observed properties are systematically well reproduced by our model our formalism allows us to introduce the static concept of extensive and intensive bias defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights with respect to a reference case where only strengths are enforced our findings complement the existing economic literature on dynamic intensive and extensive trade margins more generally they show that real world multiplexes can be strongly shaped by layer specific local constraints

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

the k user vector gaussian multiple access channel with general messages sets capacity polymatroidal structure and efficient computation the capacity region of the k user vector gaussian multiple access channel with general message sets is established furthermore due to the presence of convexity both in the discrete and continuous senses it is shown that this capacity region is efficiently computable the capacity result is obtained by specializing recent results by the authors for the discrete memoryless multiple access channel and demonstrating that it suffices to only consider jointly gaussian input and auxiliary random variables for this second conclusion it is shown that jointly gaussian random variables maximize entropy subject to lattice conditional independence and covariance constraints a result that is of interest in its own right discrete convexity arises since the capacity region is a union of polymatroids over each polymatroid computing the maximal weighted sum rates is simple due to submodularity a discrete analog of concavity of the set function associated with the linear inequalities that define the polymatroid continuous convexity arises as the set of admissible covariance matrices is convex and the polymatroidal bounds are concave in these covariances

accuracy analysis of measurements on a stable power law distributed series of events we investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined the model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events this leads to a scale free discrete random process where customary measures such as mean value and variance do not exist however converting the number of events occurring in fixed time intervals to a 1 bit clipped process allows the construction of well behaved statistics that still retain vestiges of the original power law and fluctuation properties these statistics include the clipped mean and correlation function from measurements of which both the power law index of the distribution of events and the time constant of its fluctuations can be deduced we report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process this indicates that for a fixed experiment time the error on measurements of the sample mean is minimized by an optimum choice of the number of samples it is shown furthermore that this choice is sensitive to the power law index and that the approach to poisson statistics is dominated by rare events or outliers our results are supported by numerical simulation

three state majority vote model on square lattice abstract here a non equilibrium model with two states 1 1 and a noise q on simple square lattices proposed for m j oliveira 1992 following the conjecture of up down symmetry of grinstein and colleagues 1985 is studied and generalized this model is well known today as the majority vote model they showed through monte carlo simulations that their obtained results fall into the universality class of the equilibrium ising model on a square lattice in this work we generalize the majority vote model for a version with three states now including the zero state 1 0 1 in two dimensions using monte carlo simulations we showed that our model falls into the universality class of the spin 1 1 0 1 and spin 1 2 ising model and also agree with majority vote model proposed for m j oliveira 1992 the exponent ratio obtained for our model was 1 77 3 0 121 5 and 1 1 03 5 the critical noise obtained and the fourth order cumulant were q c 0 106 5 and u 0 62 3

generating simple random graphs with prescribed degree distribution let f be a probability distribution with support on the non negative integers four methods for generating a simple undirected graph with approximate degree distribution f are described and compared two methods are based on the so called configuration model with modifications ensuring a simple graph one method is an extension of the classical erdos renyi graph where the edge probabilities are random variables and the last method starts with a directed random graph which is then modified to a simple undirected graph all methods are shown to give the correct distribution in the limit of large graph size but under different assumptions on the degree distribution f and also using different order of operations

a unifying order theoretic framework for superposition coding polymatroidal structure and optimality in the multiple access channel with general message sets two different random coding techniques both referred to as superposition coding in the literature have been widely used to obtain inner bounds for the capacity regions of various communication networks in one auxiliary codewords are generated independently and in the other they are generated in a dependent manner using the multiple access channel with general message sets as a case study we place the two techniques under a common order theoretic framework the key attribute of this framework is that it explicitly accounts for the acyclic direction and transitivity of the possible auxiliary codeword dependencies leading to three significant discoveries first with respect to a fixed coding distribution the set of rates achievable by superposition coding with dependent auxiliary codeword generation forms a polymatroid thereby generalizing the same previously known result for superposition coding with independent auxiliary codewords second we obtain a large class of superposition coding schemes by intermingling dependent and independent auxiliary codeword generation and demonstrate that the constituent polyhedral achievable rate regions are also polymatroids in each case the third discovery is that in the multiple access channel with general message sets each associated superposition coding inner bound attains the capacity region these results demonstrate a tradeoff between the complexity of dependencies in auxiliary codeword generation and that of the function that maps them into transmitted codewords

correlations in complex networks under attack for any initially correlated network after any kind of attack where either nodes or edges are removed we obtain general expressions for the degree degree probability matrix and degree distribution we show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations we find that it is possible to turn an initially assortative network into a disassortative one and vice versa by fine tuning removal of either nodes or edges for an initially uncorrelated network on the other hand we discover that only a targeted edge removal attack can induce such correlations

gas clouds rotating around a principal axis ii the separation of variables we present a new formulation of the spinning gas cloud model of ovsiannikov and dyson in the case of rotation around a fixed axis in terms of a 4 4 symmetric matrix which is a linear function of four coordinates xi we obtain a pair of separable variables l1 l2 related to the xi by a simple transformation and discuss their geometrical meaning

critical points for random boolean networks a model of cellular metabolism due to s kauffman is analyzed it consists of a network of boolean gates randomly assembled according to a probability distribution it is shown that the behavior of the network depends very critically on certain simple algebraic parameters of the distribution in some cases the analytic results support conclusions based on simulations of random boolean networks but in other cases they do not

local heuristics and the emergence of spanning subgraphs in complex networks we study the use of local heuristics to determine spanning subgraphs for use in the dissemination of information in complex networks we introduce two different heuristics and analyze their behavior in giving rise to spanning subgraphs that perform well in terms of allowing every node of the network to be reached of requiting relatively few messages and small node bandwidth for information dissemination and also of stretching paths with respect to the underlying network only modestly we contribute a detailed mathematical analysis of one of the heuristics and provide extensive simulation results on random graphs for both of them these results indicate that within certain limits spanning subgraphs are indeed expected to emerge that perform well in respect to all requirements we also discuss the spanning subgraphs inherent resilience to failures and adaptability to topological changes

scaling in animal group size distributions an elementary model of animal aggregation is presented the group size distributions resulting from this model are truncated power laws the predictions of the model are found to be consistent with data that describe the group size distributions of tuna fish sardinellas and african buffaloes

random networks with tunable degree distribution and clustering we present an algorithm for generating random networks with arbitrary degree distribution and clustering frequency of triadic closure we use this algorithm to generate networks with exponential power law and poisson degree distributions with variable levels of clustering such networks may be used as models of social networks and as a testable null hypothesis about network structure finally we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network and on the size of the giant component some analysis of these effects is presented

k core bootstrap percolation on complex networks critical phenomena and nonlocal effects we develop the theory of the k core bootstrap percolation on uncorrelated random networks with arbitrary degree distributions we show that the k core percolation is an unusual hybrid phase transition with a jump emergence of the k core as at a first order phase transition but also with a critical singularity as at a continuous transition we describe the properties of the k core explain the meaning of the order parameter for the k core percolation and reveal the origin of the specific critical phenomena we demonstrate that a so called corona of the k core plays a crucial role corona is a subset of vertices in the k core which have exactly k neighbors in the k core it turns out that the k core percolation threshold is at the same time the percolation threshold of finite corona clusters the mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point we show that a random removal of even one vertex from the k core may result in the collapse of a vast region of the k core around the removed vertex the mean size of this region diverges at the critical point we find an exact mapping of the k core percolation to a model of cooperative relaxation this model undergoes critical relaxation with a divergent rate at some critical moment

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

an anti attack model based on complex network theory in p2p networks abstract complex network theory is a useful way to study many real systems in this paper an anti attack model based on complex network theory is introduced the mechanism of this model is based on a dynamic compensation process and a reverse percolation process in p2p networks the main purpose of the paper is i a dynamic compensation process can turn an attacked p2p network into a power law pl network with exponential cutoff ii a local healing process can restore the maximum degree of peers in an attacked p2p network to a normal level iii a restoring process based on reverse percolation theory connects the fragmentary peers of an attacked p2p network together into a giant connected component in this way the model based on complex network theory can be effectively utilized for anti attack and protection purposes in p2p networks

percolation and epidemics in a two dimensional small world percolation on two dimensional small world networks has been proposed as a model for the spread of plant diseases in this paper we give an analytic solution of this model using a combination of generating function methods and high order series expansion our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of shortcuts in the small world network our results agree with scaling hypotheses and numerical simulations for the same model

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

on a class of quartic surfaces and an associated integrable differential system given a unicursal quartic in a plane and four bi tangential straight lines there exist a pair of conics four times tangential to it choosing an arbitrary point k0 outside the plane the lines and either one of the conics determine four planes and a cone and a quartic surface can be found that stays tangential to them and presents 15 conic point singularities including k0 we introduce a one parameter family of symmetric tensors which are polynomial functions of degree 7 of the cartesian coordinates each of them determines two families of curves on the surface which are the null curves of the associated metric and are the integral curves of a differential system which turns out to possess the painleve property and to be integrable by quadratures differential systems of that form have been found gaffet 2006 j phys a math gen 39 99 to represent the rotating motion with precession of gas clouds expanding into a vacuum

structure of shells in complex networks we define shell l in a network as the set of nodes at distance l with respect to a given node and define rl as the fraction of nodes outside shell l in a transport process information or disease usually diffuses from a random node and reach nodes shell after shell thus understanding the shell structure is crucial for the study of the transport property of networks we study the statistical properties of the shells of a randomly chosen node for a randomly connected network with given degree distribution we derive analytically the degree distribution and average degree of the nodes residing outside shell l as a function of rl further we find that rl follows an iterative functional form rl phi rl 1 where phi is expressed in terms of the generating function of the original degree distribution of the network our results can explain the power law distribution of the number of nodes bl found in shells with l larger than the network diameter d which is the average distance between all pairs of nodes for real world networks the theoretical prediction of rl deviates from the empirical rl we introduce a network correlation function c rl identical with rl phi rl 1 to characterize the correlations in the network where rl is the empirical value and phi rl 1 is the theoretical prediction c rl 1 indicates perfect agreement between empirical results and theory we apply c rl to several model and real world networks we find that the networks fall into two distinct classes i a class of poorly connected networks with c rl 1 where a larger smaller fraction of nodes resides outside inside distance l from a given node than in randomly connected networks with the same degree distributions examples include the watts strogatz model and networks characterizing human collaborations such as citation networks and the actor collaboration network ii a class of well connected networks with c rl 1 examples include the barabasi albert model and the autonomous system internet network

networks matroids and non shannon information inequalities we define a class of networks called matroidal networks which includes as special cases all scalar linearly solvable networks and in particular solvable multicast networks we then present a method for constructing matroidal networks from known matroids we specifically construct networks that play an important role in proving results in the literature such as the insufficiency of linear network coding and the unachievability of network coding capacity we also construct a new network from the vamos matroid which we call the vamos network and use it to prove that shannon type information inequalities are in general not sufficient for computing network coding capacities to accomplish this we obtain a capacity upper bound for the vamos network using a non shannon type information inequality discovered in 1998 by zhang and yeung and then show that it is smaller than any such bound derived from shannon type information inequalities this is the first application of a non shannon type inequality to network coding we also compute the exact routing capacity and linear coding capacity of the vamos network finally using a variation of the vamos network we prove that shannon type information inequalities are insufficient even for computing network coding capacities of multiple unicast networks

covering problems and core percolations on hypergraphs we introduce two generalizations of core percolation in graphs to hypergraphs related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs respectively we offer analytical solutions of these two core percolations for uncorrelated random hypergraphs whose vertex degree and hyperedge cardinality distributions are arbitrary but have nondiverging moments we find that for several real world hypergraphs their two cores tend to be much smaller than those of their null models suggesting that covering problems in those real world hypergraphs can actually be solved in polynomial time

percolation on correlated networks we reconsider the problem of percolation on an equilibrium random network with degree degree correlations between nearest neighboring vertices focusing on critical singularities at a percolation threshold we obtain criteria for degree degree correlations to be irrelevant for critical singularities we present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents

patterns in randomly evolving networks idiotypic networks we present a model for the evolution of networks of occupied sites on undirected regular graphs at every iteration step in a parallel update i randomly chosen empty sites are occupied and occupied sites having occupied neighbor degree outside of a given interval t l t u are set empty depending on the influx i and the values of both lower threshold and upper threshold of the occupied neighbor degree different kinds of behavior can be observed in certain regimes stable long living patterns appear we distinguish two types of patterns static patterns arising on graphs with low connectivity and dynamic patterns found on high connectivity graphs increasing i patterns become unstable and transitions between almost stable patterns interrupted by disordered phases occur for still larger i the lifetime of occupied sites becomes very small and network structures are dominated by randomness we develop methods to analyze the nature and dynamics of these network patterns give a statistical description of defects and fluctuations around them and elucidate the transitions between different patterns results and methods presented can be applied to a variety of problems in different fields and a broad class of graphs aiming chiefly at the modeling of functional networks of interacting antibodies and b cells of the immune system idiotypic networks we focus on a class of graphs constructed by bit chains the biological relevance of the patterns and possible operational modes of idiotypic networks are discussed

revealing the microstructure of the giant component in random graph ensembles the microstructure of the giant component of the erd s renyi network and other configuration model networks is analyzed using generating function methods while configuration model networks are uncorrelated the giant component exhibits a degree distribution which is different from the overall degree distribution of the network and includes degree degree correlations of all orders we present exact analytical results for the degree distributions as well as higher order degree degree correlations on the giant components of configuration model networks we show that the degree degree correlations are essential for the integrity of the giant component in the sense that the degree distribution alone cannot guarantee that it will consist of a single connected component to demonstrate the importance and broad applicability of these results we apply them to the study of the distribution of shortest path lengths on the giant component percolation on the giant component and spectra of sparse matrices defined on the giant component we show that by using the degree distribution on the giant component one obtains high quality results for these properties which can be further improved by taking the degree degree correlations into account this suggests that many existing methods currently used for the analysis of the whole network can be adapted in a straightforward fashion to yield results conditioned on the giant component

dynamics of epidemics on random networks this paper examines how diseases on random networks spread in time the disease is described by a probability distribution function for the number of infected and recovered individuals and the probability distribution is described by a generating function the time development of the disease is obtained by iterating the generating function in cases where the disease can expand to an epidemic the probability distribution function is the sum of two parts one that is static at long times and another whose mean grows exponentially the time development of the mean number of infected individuals is obtained analytically when epidemics occur the probability distributions are very broad and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

enhancing consensus in weighted networks with coupling time delay abstract we study the consensus problem in a weighted and directed network composed of self propelled agents the weight which quantifies the relationship between the agents is adjusted according to their state incoherence to suppress the heterogeneity in state the proposed consensus protocol enhances the convergence efficiency of consensus greatly and has better performance than that of two other protocols the convergence efficiency can be further improved by adjusting the parameter of this protocol furthermore the robustness of the system against coupling time delay is significantly increased unlike most consensus acceleration methods no topological information is needed in our model networks with different stuctures are investigated to demonstrate the generality of the method

hierarchical regular small world networks two new networks are introduced that resemble small world properties these networks are recursively constructed but retain a fixed regular degree they possess a unique one dimensional lattice backbone overlaid by a hierarchical sequence of long distance links mixing real space and small world features both networks one 3 regular and the other 4 regular lead to distinct behaviors as revealed by renormalization group studies the 3 regular network is planar has a diameter growing as with system size n and leads to super diffusion with an exact anomalous exponent dw 1 306 but possesses only a trivial fixed point tc 0 for the ising ferromagnet in turn the 4 regular network is non planar has a diameter growing as exhibits ballistic diffusion dw 1 and a non trivial ferromagnetic transition tc 0 it suggests that the 3 regular network is still quite geometric while the 4 regular network qualifies as a true small world with mean field properties as an engineering application we discuss synchronization of processors on these networks

a modified vicsek model for self propelled agents with exponential neighbor weight and restricted visual field abstract large flocks of wild beings can have coordinated motion with neither leading center nor global information the vicsek model and its new versions explained such collective behavior of self propelled agents with the mechanism of un weighted influence of neighbors and global visual field gvf which may not always fit the reality in the present work we take both exponential neighbor weight enw and restricted visual field rvf into account and investigate the combinatory effect of them based on this mechanism in most cases of our simulation stationary direction consensus v a exhibits a maximum or decreases with v f and a minimum convergence time t m i n appears in rvf which demonstrates that gvf is not necessary for coordinated motion while rvf matched enw would be reasonable moreover we simulated various recipes for optimizing v a and t in unfavorable cases and found critical points separating inverse dependent variations of t the present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature

on the likelihood of forests abstract how complex a network is crucially impacts its function and performance in many modern applications the networks involved have a growth property and sparse structures which pose challenges to physicists and applied mathematicians in this paper we introduce the forest likelihood as a plausible measure to gauge how difficult it is to construct a forest in a non preferential attachment way based on the notions of admittable labeling and path construction we propose algorithms for computing the forest likelihood of a given forest concrete examples as well as the distributions of forest likelihoods for all forests with some fixed numbers of nodes are presented moreover we illustrate the ideas on real life networks including a benzenoid tree a mathematical family tree and a peer to peer network

phase transitions on markovian bipartite graphs an application of the zero range process we analyze the existence and the size of the giant component in the stationary state of a markovian model for bipartite multigraphs in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero range process the degrees being static on the other set the analysis is based on approximations by independent variables and on the results of molloy and reed for graphs with prescribed degree sequences the possible types of phase diagrams are identified by studying the behavior below the zero range condensation point as a specific example we consider the so called evans interaction in particular we examine the values of a critical exponent describing the growth of the giant component as the value of the dilution parameter controlling the connectivity is increased above the critical threshold rigorous analysis spans a large portion of the parameter space of the model exactly at the point of zero range condensation these results supplemented with conjectures supported by monte carlo simulations suggest that the phenomenological landau theory for percolation on graphs is not broken by the fluctuations