Search

We prove strong consistency of spectral clustering under the degree-corrected hypergraph stochastic block model in the sparse regime where the maximum expected hyperdegree is as small as $\Omega(\log n)$ with $n$ denoting the number of nodes. We show that the basic spectral clustering without preprocessing or postprocessing is strongly consistent in an even wider range of the model parameters, in contrast to previous studies that either trim high-degree nodes or perform local refinement. At the heart of our analysis is the entry-wise eigenvector perturbation bound derived by the leave-one-out technique. To the best of our knowledge, this is the first entry-wise error bound for degree-corrected hypergraph models, resulting in the strong consistency for clustering non-uniform hypergraphs with heterogeneous hyperdegrees., Comment: 16 pages, 1 figures

Many real-world systems involving higher-order interactions can be modeled by hypergraphs, where vertices represent the systemic units and hyperedges describe the interactions among them. In this paper, we focus on the problem of hyperlink prediction which aims at inferring missing hyperlinks based on observed hyperlinks. We propose three similarity indices for hyperlink prediction based on local random walks and Jensen-Shannon divergence. Numerical experiments show that the proposed indices outperform the state-of-the-art methods on a broad range of datasets., Comment: IoP Latex, 15 pages, 1 figures

The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on hypergraphs. To understand how high-order interactions affect the breakdown of the system, we develop a theoretical framework based on generating function technology to derive the cascade condition and the giant component of vulnerable vertices, which depend on both hyperedges and hyperdegrees. First, we find a dual role of the hyperedge in propagation: when the average hyperdegree is small, increasing the size of the hyperedges may make the system fragile, while the average hyperdegree is relatively large, the increase of the hyperedges causes the system to be robust. Then, we identify the effects of threshold, hyperdegree, and hyperedge heterogeneities. The heterogeneity of individual thresholds causes the system to be more fragile, while the heterogeneity of individual hyperdegrees or hyperedges increases the robustness of the system. Finally, we show that the higher hyperdegree a vertex has, the larger possibility and faster speed it will get activated. We verify these results by simulating meme spreading on both random hypergraph models and hypergraphs constructed from empirical data., Comment: revtex

Characterizing temporal evolution of stock markets is a fundamental and challenging problem. The literature on analyzing the dynamics of the markets has focused so far on macro measures with less predictive power. This paper addresses this issue from a micro point of view. Given an investigating period, a series of stock networks are constructed first by the moving-window method and the significance test of stock correlations. Then, several conserved networks are generated to extract different backbones of the market under different states. Finally, influential stocks and corresponding sectors are identified from each conserved network, based on which the longitudinal analysis is performed to describe the evolution of the market. The application of the above procedure to stocks belonging to Standard \& Pool's 500 Index from January 2006 to April 2010 recovers the 2008 financial crisis from the evolutionary perspective., Comment: latex, 16 pages, 1 figure, 14 tables

Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the number of communities. Here we propose an efficient hypothesis test for community detection based on quantifying dissimilarities between graphs. Given a random graph, the null hypothesis is that it is of degree-corrected Erd\"{o}s-R\'{e}nyi type. We compare the dissimilarity between them by a measure incorporating the vertex distance distribution, the clustering coefficient distribution, and the alpha-centrality distribution, which is used for our hypothesis test. We design a two-stage bipartitioning algorithm to uncover the number of communities and the corresponding structure simultaneously. Experiments on synthetic and real networks show that our method outperforms state-of-the-art ones., Comment: a algorithm has been added

Although the threshold network is one of the most used tools to characterize the underlying structure of a stock market, the identification of the optimal threshold to construct a reliable stock network remains challenging. In this paper, the concept of dynamic consistence between the threshold network and the stock market is proposed. The optimal threshold is estimated by maximizing the consistence function. The application of this procedure to stocks belonging to Standard \& Pool's 500 Index from January 2006 to December 2011 yields the threshold value 0.28. In analyzing topological characteristics of the generated network, three globally financial crises can be distinguished well from the evolutionary perspective., Comment: latex, 16 pages, 6 figures

The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense., Comment: 12 pages, 7 figures

In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at a microscopic level. However, a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking. We study a susceptible-infected-susceptible epidemic model with imperfect vaccination on dynamic contact networks, where the macroscopic intervention is represented by random vaccination of the population and the microscopic protection is characterised by susceptible individuals rewiring contacts from infective neighbours. In particular, the model is formulated both in populations without and then with demographic effects. Using the pairwise approximation and the probability generating function approach, we investigate both dynamics of the epidemic and the underlying network. For populations without demography, the emerging degree correlations, bistable states, and oscillations demonstrate the combined effects of the public vaccination program and individual protective behavior. Compared to either strategy in isolation, the combination of public vaccination and individual protection is more effective in preventing and controlling the spread of infectious diseases by increasing both the invasion threshold and the persistence threshold. For populations with additional demographic factors, the integration between vaccination intervention and individual rewiring may promote epidemic spreading due to the birth effect. Moreover, the degree distributions of both networks in the steady state is closely related to the degree distribution of newborns, which leads to uncorrelated connectivity. All the results demonstrate the importance of both local protection and global intervention, as well as the demographic effects., Comment: 36 pages, 12 figures, 2 tables, Springer-tex (SVJour3 document class)

Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent behaviour in one region because of the invasion from an endemic population elsewhere. In this paper we address this issue and study a susceptible-infected-susceptible epidemiological model on a network consisting of two communities, where the disease is endemic in one community but alternates between outbreaks and extinctions in the other. We provide a detailed characterization of the temporal dynamics of epidemic patterns in the latter community. In particular, we investigate the time duration of both outbreak and extinction, and the time interval between two consecutive inter-community infections, as well as their frequency distributions. Based on the mean-field theory, we theoretically analyze these three timescales and their dependence on the average node degree of each community, the transmission parameters, and the number of intercommunity links, which are in good agreement with simulations, except when the probability of overlaps between successive outbreaks is too large. These findings aid us in better understanding the bursty nature of disease spreading in a local community, and thereby suggesting effective time-dependent control strategies., Comment: 21 pages, 10 figures, IoP-tex

Whether a scientific paper is cited is related not only to the influence of its author(s) but also to the journal publishing it. Scientists, either proficient or tender, usually submit their most important work to prestigious journals which receives higher citations than the ordinary. How to model the role of scientific journals in citation dynamics is of great importance. In this paper we address this issue through two folds. One is the intrinsic heterogeneity of a paper determined by the impact factor of the journal publishing it. The other is the mechanism of a paper being cited which depends on its citations and prestige. We develop a model for citation networks via an intrinsic nodal weight function and an intuitive ageing mechanism. The node's weight is drawn from the distribution of impact factors of journals and the ageing transition is a function of the citation and the prestige. The node-degree distribution of resulting networks shows nonuniversal scaling: the distribution decays exponentially for small degree and has a power-law tail for large degree, hence the dual behaviour. The higher the impact factor of the journal, the larger the tipping point and the smaller the power exponent that are obtained. With the increase of the journal rank, this phenomenon will fade and evolve to pure power laws., Comment: 14 pages, 6 figures, Latex

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barab\'asi-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations., Comment: 11 pages, 8 figures, RevTex4

In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model., Comment: ws-tex, 11 pages, 5 figures

Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree., Comment: IoP Style

We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, a vertex $i$ is assigned a fitness $x_i$, drawn from a given probability distribution function $f(x)$. During network evolution, with rate $p$ we add a vertex $j$ of fitness $x_j$ and connect to an existing vertex $i$ of fitness $x_i$ selected preferentially to a linking probability function $g(x_i,x_j)$ which depends on the fitnesses of the two vertices involved and, with rate $1-p$ we create an edge between two already existed vertices with fitnesses $x_i$ and $x_j$, with a probability also preferential to the connection function $g(x_i,x_j)$. For the proper choice of $g$, the resulting networks have generalized power laws, irrespective of the fitness distribution of vertices., Comment: ws-ijmpc.tex

A rank-dependent deactivation mechanism is introduced to network evolution. The growth dynamics of the network is based on a finite memory of individuals, which is implemented by deactivating one site at each time step. The model shows striking features of a wide range of real-world networks: power-law degree distribution, high clustering coefficient, and disassortative degree correlation., Comment: 5 pages, 5 figures, RevTex4

The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes' degrees., Comment: 9 pages, 2 figures, Latex Style

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations., Comment: 4 pages, 3 figures

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks., Comment: 14 pages, 6 figures

We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of neuron state disrupts the adjustment of the rhythm of neuron oscillation and prevents further increase of firing synchronization., Comment: 8 pages, 8 figures

We investigate the standard susceptible-infected-susceptible model on a random network to study the effects of preference and geography on diseases spreading. The network grows by introducing one random node with $m$ links on a Euclidean space at unit time. The probability of a new node $i$ linking to a node $j$ with degree $k_j$ at distance $d_{ij}$ from node $i$ is proportional to $k_{j}^{A}/d_{ij}^{B}$, where $A$ and $B$ are positive constants governing preferential attachment and the cost of the node-node distance. In the case of A=0, we recover the usual epidemic behavior with a critical threshold below which diseases eventually die out. Whereas for B=0, the critical behavior is absent only in the condition A=1. While both ingredients are proposed simultaneously, the network becomes robust to infection for larger $A$ and smaller $B$., Comment: 4 pages, 5 figures, submitted to Phys. Rev. E

The emergence and maintenance of cooperation within sizable groups of unrelated humans offer many challenges for our understanding. We propose that the humans' capacity of communication, such as how many and how far away the fellows can build up mutual communications, may affect the evolution of cooperation. We study this issue by means of the public goods game (PGG) with a two-layered network of contacts. Players obtain payoffs from five-person public goods interactions on a square lattice (the interaction layer). Also, they update strategies after communicating with neighbours in learning layer, where two players build up mutual communication with a power law probability depending on their spatial distance. Our simulation results indicate that the evolution of cooperation is indeed sensitive to how players choose others to communicate with, including the amount as well as the locations. The tendency of localised communication is proved to be a new mechanism to promote cooperation., Comment: 6 pages, 4 figures

The response of degree-correlated scale-free attractor networks to stimuli is studied. We show that degree-correlated scale-free networks are robust to random stimuli as well as the uncorrelated scale-free networks, while assortative (disassortative) scale-free networks are more (less) sensitive to directed stimuli than uncorrelated networks. We find that the degree-correlation of scale-free networks makes the dynamics of attractor systems different from uncorrelated ones. The dynamics of correlated scale-free attractor networks result in the effects of degree correlation on the response to stimuli., Comment: 5 pages, 5 figures

We study the excitable Greenberg-Hastings cellular automaton model on scale-free networks. We obtained analytical expressions for no external stimulus and the uncoupled case. It is found that the curves, the average activity $F$ versus the external stimulus rate $r$, can be fitted by a Hill function, but not exactly, and there exists a relation $F\propto r^\alpha$ for the low-stimulus response, where Stevens-Hill exponent $\alpha$ ranges from $\alpha = 1$ in the subcritical regime to $\alpha = 0.5$ at criticality. At the critical point, the range reaches the maximal. We also calculate the average activity $F^{k}(r)$ and the dynamic range $\Delta^{k}(p)$ for nodes with given connectivity $k$. It is interesting that nodes with larger connectivity have larger optimal range, which could be applied in biological experiments to reveal the network topology., Comment: submitted to Phys. Rev. E

We study the effects of the degree distribution in mutual synchronization of two-layer neural networks. We carry out three coupling strategies: large-large coupling, random coupling, and small-small coupling. By computer simulations and analytical methods, we find that couplings between nodes with large degree play an important role in the synchronization. For large-large coupling, less couplings are needed for inducing synchronization for both random and scale-free networks. For random coupling, cutting couplings between nodes with large degree is very efficient for preventing neural systems from synchronization, especially when subnetworks are scale-free., Comment: 5 pages, 4 figures

We introduce nonlinear attractive effects into a spatial Prisoner's Dilemma game where the players located on a square lattice can either cooperate with their nearest neighbors or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbors with a probability proportional to $\mathcal{A}^\alpha$ denoting the attractiveness of the neighbor, where $\mathcal{A}$ is the payoff collected by it and $\alpha$ ($\geq$0) is a free parameter characterizing the extent of the nonlinear effect; and then adopting its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density $\rho_C$ of cooperators in the stationary state for different values of $\alpha$. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect. In particular, for large values of $\alpha$, i.e., strong nonlinear attractive effects, the system exhibits two absorbing states (all cooperators or all defectors) separated by an active state (coexistence of cooperators and defectors) when varying the temptation to defect. In the critical region where $\rho_C$ goes to zero, the extinction behavior is power law-like $\rho_C$ $\sim$ $(b_c-b)^{\beta}$, where the exponent $\beta$ accords approximatively with the critical exponent ($\beta\approx0.584$) of the two-dimensional directed percolation and depends weakly on the value of $\alpha$., Comment: 7 pages, 4 figures

Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the network is, the more highly the epidemic prevails., Comment: 4 pages, 5 figures

We study geographical effects on the spread of diseases in lattice-embedded scale-free networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard Susceptible-Infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads.

We carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square displacement, and the network coverage for unrestricted random walk. The diffusions both on DANs and RANs are proved to be sublinear. The search efficiency for walks with various strategies and the influence of the topology of underlying networks on the dynamics of walks are discussed. Contrary to one's intuition, it is shown that the self-avoiding random walk, which has been verified as an optimal strategy for searching on scale-free and small-world networks, is not the best strategy for the DAN in the thermodynamic limit., Comment: 5 pages, 4 figures

We present a new interpretation for encoding information of the period of input signals into spike-trains in individual sensory neuronal systems. The spike-train could be described as the waveform sample of the input signal which locks sample points to wave crests with randomness. Based on simulations of the Hodgkin-Huxley (HH) neuron responding to periodic inputs, we demonstrate that the random sampling is a proper encoding method in medium frequency region since power spectra of the reconstructed spike-trains are identical to that of neural signals., Comment: 4 pages, 4 figures