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Abstract When analyzing and describing the statistical and topological characteristics of complex networks, the heterogeneity can provide profound and systematical recognition to illustrate the difference of individuals, and many node significance indices have been investigated to describe heterogeneity in different perspectives. In this paper a new node heterogeneity index based on the von Neumann entropy is proposed, which allows us to investigate the differences of nodes features in the view of spectrum eigenvalues distribution, and examples in reality networks present its great performance in selecting crucial individuals. Then to lower down the computational complexity, an approximation calculation to this index is given which only depends on its first and second neighbors. Furthermore, in reducing the network heterogeneity index by Estrada, this entropy heterogeneity presents excellent efficiency in Erdös–Rényi and scale-free networks compared to other node significance measurements; in reducing the average clustering coefficient, this node entropy index could break down the cluster structures efficiently in random geometric graphs, even faster than clustering coefficient itself. This new methodology reveals the node heterogeneity and significance in the perspective of spectrum, which provides a new insight into networks research and performs great potentials to discover essential structural features in networks. Highlights • A new definition of node heterogeneity measurement based on von Neumann entropy. • Examples and experiments on real-world networks. • An approximation method to calculate the entropy. • Experiments on reducing the Estrada heterogeneity index. • Experiments on reducing the average clustering coefficient. [ABSTRACT FROM AUTHOR]

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer. [ABSTRACT FROM AUTHOR]

Information diffusion dynamics in complex networks is often modeled as a contagion process among neighbors which is analogous to epidemic diffusion. The attention of previous literature is mainly focused on epidemic diffusion within one network, which, however neglects the possible interactions between nodes beyond the underlying network. The disease can be transmitted to other nodes by other means without following the links in the focal network. Here we account for this phenomenon by introducing the independent spreaders in a susceptible–infectious–recovered contagion process. We derive the critical epidemic thresholds on Erdős–Rényi and scale-free networks as a function of infectious rate, recovery rate and the activeness of independent spreaders. We also present simulation results on ER and SF networks, as well as on a real-world email network. The result shows that the extent to which a disease can infect might be more far-reaching, than we can explain in terms of link contagion only. Besides, these results also help to explain how activeness of independent spreaders can affect the diffusion process, which can be used to explore many other dynamical processes. [ABSTRACT FROM AUTHOR]

Boolean network has been widely used in modeling biological systems and one of the key problems is its stability in response to small perturbations. Based on the hypothesis that the states of all nodes are homogenously updated, great progress has been made in previous works. In real biological networks, however, the updates of genes typically show much heterogeneity. To address such conditions, we introduce transmission sensitivity into Boolean network model. By the method of semi-annealed approximation, we illustrate that in a homogenous network, the critical condition of stability has no connection with its transmission sensitivity. As for heterogeneous networks, it reveals that correlations between network topology and transmission sensitivity can have profound effects on the its stability. This result shows a new mechanism that affects the stability of Boolean network, which could be used to control the dynamics in real biological systems. [ABSTRACT FROM AUTHOR]

Identifying highly susceptible individuals in spreading processes is of great significance in controlling outbreaks. In this paper, we explore the susceptibility of people in susceptible-infectious-recovered (SIR) and rumor spreading dynamics. We first study the impact of community structure on people’s susceptibility. Although the community structure can reduce the number of infected people for same infection rate, it will not significantly affect nodes’ susceptibility. We find the susceptibility of individuals is sensitive to the choice of spreading dynamics. For SIR spreading, since the susceptibility is highly correlated to nodes’ influence, the topological indicator k -shell can better identify highly susceptible individuals, outperforming degree, betweenness centrality and PageRank. In contrast, in rumor spreading model, where nodes’ susceptibility and influence have no clear correlation, degree performs the best among considered topological measures. Our finding highlights the significance of both topological features and spreading mechanisms in identifying highly susceptible population. [ABSTRACT FROM AUTHOR]

Recent studies of rumor or information diffusion process in complex networks show that in contrast to traditional comprehension, individuals who participate in rumor spreading within one network do not always get the rumor from their neighbors. They can obtain the rumor from different sources like online social networks and then publish it on their personal sites. In our paper, we discuss this phenomenon in complex networks by adopting the concept of independent spreaders. Rather than getting the rumor from neighbors, independent spreaders learn it from other channels. We further develop the classic “ignorant-spreaders-stiflers” or SIR model of rumor diffusion process in complex networks. A steady-state analysis is conducted to investigate the final spectrum of the rumor spreading under various spreading rate, stifling rate, density of independent spreaders and average degree of the network. Results show that independent spreaders effectively enhance the rumor diffusion process, by delivering the rumor to regions far away from the current rumor infected regions. And though the rumor spreading process in SF networks is faster than that in ER networks, the final size of rumor spreading in ER networks is larger than that in SF networks. [ABSTRACT FROM AUTHOR]

Nowadays the propagation of human activity, especially health behavior, has become a significant issue in the study of online social network. Considering the effect of human behavior on information diffusion in social networks (Centola, 2010), we propose a simple “susceptible–adopted–susceptible” model with several interpretable parameters. This model shows a similar diminishing returns effect, in which the adoption probability of a susceptible individual grows less quickly as the number of his or her adopted neighbors increases. Surprisingly, the model’s contagion threshold is merely decided by the spreading rate and logout probability, not affected by the similar diminishing returns effect in real cases. Moreover, we find that the augmentation of the similar diminishing returns factor can increase the spreading speed and coverage. Our model captures properties of the real spreading of health behavior in real online networks and can provide instructions for fast propagation of new health behavior. [ABSTRACT FROM AUTHOR]

Non-periodic phenomena are common in a wide range of real-world recurrent dynamics, such as the occasional pandemic of seasonal influenza and the abrupt collapse of stock markets. In this paper we propose a biased excitable network model and illustrate the non-periodic phenomena as the collective response of a large amount of excitable individuals. In contrast with classic excitable networks, we introduce the bias of external stimuli that affects the exact behavior of each individual rather than its own inherent property. Based on the locally tree-like topology, we make a second order approximation on the network activity with diminishing stimuli. Result shows that the self-sustainment of network dynamics is determined by the largest eigenvalue λ of the weighted adjacent matrix. For λ > 1 the network is self-sustained even if the stimuli intensity approaches zero. For λ < 1 , the system tends to end up in quiescent state. At critical condition λ = 1 , the dynamic range of the system, which is the range of stimuli intensity that is distinguishable according to network activity, reaches maximum value. We also find that the dynamic range can be further enhanced when nodes are more inclined to inhibitory state as a result of smaller stimuli bias. These results are well supported by numerical simulations on both synthetic and real-world networks. Based on the proposed model, we manage to reproduce similar non-periodic phenomena to those in real-world recurrent dynamics, even when the intensity of external stimuli remains constant. Our research shed light on the mechanism of non-periodic phenomena in recurrent dynamics, which can be applied to the prevention of epidemic outbreaks as well as financial crisis. • The bias of external stimuli affects the behavior of each individual. • The largest eigenvalue λ of weighted adjacent matrix determines network sustainment. • The dynamic range reaches maximum at λ = 1. • The dynamic range can be further enhanced by smaller stimuli bias. [ABSTRACT FROM AUTHOR]

Abstract: Group interactions on structured populations can be represented by the public goods game on networks. During the evolutionary games, selective investment mechanism fosters social cooperative behavior. First we focus on star-like graphs to provide some light on why selective investment mechanism can promote collective cooperation. Then we implement public goods game with this mechanism on scale free networks to investigate behavior properties of individuals within different social environments. We indicate that high-degree nodes are predominantly inert owning largely to their satisfaction with their status, while low-degree nodes are very active due to their strive towards higher prosperity. Besides, we introduce the Gini coefficient to describe social inequality and find that large multiply factor favors social fairness. Our work is applicable for community supervision and social wealth regulation. [Copyright &y& Elsevier]

Abstract: Rumor diffusion on complex networks has been widely investigated assuming that an individual learns the rumor merely from its neighbors, which, however, is not always the case. Recent studies of layered models have shown that individuals belonging to many different networks can affect the spreading process on one network. In this paper, we take this phenomenon into consideration and discuss its influence on rumor diffusion in complex networks by introducing independent spreaders. Independent spreaders are nodes that know the rumor from other channels rather than their neighbors. A new stochastic technique is used to obtain the dynamics of rumor diffusion. Results reveal that independent spreaders boost the process by bringing the rumor to regions remote from current spreaders. In order to accelerate diffusion, we find that improving the network connectivity is more efficient than adding more independent spreaders. [Copyright &y& Elsevier]

Abstract: The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites. [Copyright &y& Elsevier]

Abstract: Recently, the modified BFW model on random graphs [W. Chen, R.M. D’Souza, Phys. Rev. Lett. 106 (2011) 115701], which shows a discontinuous percolation transition with multiple giant components, has attracted much attention from physicists and statisticians. In this paper, by establishing the evolution equations on the modified BFW model, the evolution process and steady-states on both random graphs and finite-dimensional lattices are analyzed. On a random graph, by varying the edge accepted rate , the system stabilizes in a steady-state with different numbers of giant components. Moreover, a close correspondence is built between the values of and the number of giant components in steady-states, the efficiency of which is verified by the numerical simulations. Then, the sizes of giant components for different evolution strategies can be obtained by solving some constraints derived from the evolution equations. Meanwhile, a similar analysis is expanded to finite-dimensional lattices, and we find the BFW () model on a finite-dimensional lattice has different steady-states from those on a random graph, but they have the same evolution mechanism. The analysis of the evolution process and steady-state is of great help to explain the properties of discontinuous percolation and the role of nonlocality. [Copyright &y& Elsevier]

Abstract: We investigate wealth distribution on scale-free networks with different consumption strategies. We indicate that nonlinear consumption function can lead to exponential wealth distribution with a power law tail in accordance with empirical data. In addition, we suggest that anti-degree preference and consumption promotion can make distribution more equal. This provides an effective and practical way to optimize the equality of wealth distribution. [Copyright &y& Elsevier]

Abstract: Most real-world networks from various fields share a universal topological property as community structure. In this paper, we propose a node-similarity based mechanism to explore the formation of modular networks by applying the concept of hidden metric spaces of complex networks. It is demonstrated that network community structure could be formed according to node similarity in the underlying hidden metric space. To clarify this, we generate a set of observed networks using a typical kind of hidden metric space model. By detecting and analyzing corresponding communities both in the observed network and the hidden space, we show that the values of the fitness are rather close, and the assignments of nodes for these two kinds of community structures detected based on the fitness parameter are extremely matching ones. Furthermore, our research also shows that networks with strong clustering tend to display prominent community structures with large values of network modularity and fitness. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure -cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a non-interacting boson model to investigate the topological structure of complex networks. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of realistic networks. We find that the ground-state degeneracy of this model is equal to the number of connected components in a network and the square of each coefficient in the expansion of the ground state gives the average time that a random walker spends at each node in the infinite time limit. To show the usefulness of this approach in practice, we also carry out numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods. Furthermore, we show that the first excited state appears always on the largest connected component of the network. The relationship between the first excited energy and the average shortest path length in networks is also discussed. [Copyright &y& Elsevier]

The dynamical process of epidemics has been a widely discussed topic in the study of complex networks and public health. While previous literature has focused mostly on the strict link-contagion through individual connections, the complex system in which diffusion dynamics takes place usually has many latent relations that could foster the spread process. Here we account for this phenomenon by investigating the epidemic SIS (Susceptible–Infected–Susceptible) with participation of independent spreaders. We derive the theoretical expressions of the dynamical systems and obtain the critical threshold of extensive diffusion, in both homogeneous and heterogeneous networks. We also perform a range of computational simulations, and show that the role independent spreaders play in such scenarios is huge by infecting remote areas in the network. • We introduce the independent spreaders in a susceptible-infectious- susceptible epidemic model in complex networks. • We derive the critical epidemic thresholds on ER and scale-free networks as a function of infectious rate, recovery rate and the activeness of independent spreaders. • Combining with simulations, we exhibit that the extent to which a disease can infect might be more far-reaching than we can explain when we only account for link contagion. [ABSTRACT FROM AUTHOR]