arXiv subjects

Zengru Di

Publications and source records attributed to Zengru Di.

At least 73 records · Page 4Linked to original sources

arXiv2011

Toward a General Understanding of the Scaling Laws in Human and Animal Mobility

Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general optimization model, a random walker following scaling laws (whose traveling distances in each step obey a power law distribution with exponent α) tries to diversify its visiting places under a given total traveling distance with a home-return probability. The results show that different optimal exponents in between 1 and 2 can emerge naturally. Therefore, the scaling property of human and animal mobility can be understood in our framework where the discrepancy of the scaling law exponents is due to the home-return constraint under the maximization of the visiting places diversity.

physics.bio-ph↗

arXiv2011

Detecting Important Nodes to Community Structure Using the Spectrum of the Graph

Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem. In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change in the eigenvalues of the network adjacency matrix upon their removal. Second, we also propose an index to distinguish two kinds of important nodes in communities, i.e., "community core" and "bridge". Our indices are only relied on the spectrum of the graph matrix. They are applied in many artificial networks as well as many real-world networks. This new methodology gives us a basic approach to solve this challenging problem and provides a realistic result.

physics.soc-ph↗

arXiv2011

Onset of Synchronization in Weighted Complex Networks: the Effect of Weight-Degree Correlation

By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.

nlin.CD↗

arXiv2011

Detecting the optimal number of communities in complex networks

To obtain the optimal number of communities is an important problem in detecting community structure. In this paper, we extend the measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic $Ω(c)$ is proposed to detect the optimal number of communities. In general, when $Ω(c)$ reaches its local maximum, especially the first one, the corresponding number of communities \emph{c} is likely to be optimal in community detection. Moreover, the statistic $Ω(c)$ can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index $Ω(c)$ is effective in both artificial and real world networks.

physics.soc-ph↗

arXiv2011

Navigation in non-uniform density social networks

Recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $d$ scales as $P(d)\propto d^{-1}$. Since population density is non-uniform in real social networks, a scale invariant friendship network(SIFN) based on the above empirical law is introduced to capture this phenomenon. We prove the time complexity of navigation in 2-dimensional SIFN is at most $O(\log^4 n)$. In the real searching experiment, individuals often resort to extra information besides geography location. Thus, real-world searching process may be seen as a projection of navigation in a $k$-dimensional SIFN($k>2$). Therefore, we also discuss the relationship between high and low dimensional SIFN. Particularly, we prove a 2-dimensional SIFN is the projection of a 3-dimensional SIFN. As a matter of fact, this result can also be generated to any $k$-dimensional SIFN.

physics.soc-ph↗

arXiv2011

Exact Solution for Optimal Navigation with Total Cost Restriction

Recently, Li \textit{et al.} have concentrated on Kleinberg's navigation model with a certain total length constraint $Λ= cN$, where $N$ is the number of total nodes and $c$ is a constant. Their simulation results for the 1- and 2-dimensional cases indicate that the optimal choice for adding extra long-range connections between any two sites seems to be $α=d+1$, where $d$ is the dimension of the lattice and $α$ is the power-law exponent. In this paper, we prove analytically that for the 1-dimensional large networks, the optimal power-law exponent is $α=2$ Further, we study the impact of the network size and provide exact solutions for time cost as a function of the power-law exponent $α$. We also show that our analytical results are in excellent agreement with simulations.

physics.soc-ph↗

arXiv2010

Enhancing synchronization by directionality in complex networks

We proposed a method called residual edge-betweenness gradient (REBG) to enhance synchronizability of networks by assignment of link direction while keeping network topology and link weight unchanged. Direction assignment has been shown to improve the synchronizability of undirected networks in general, but we find that in some cases incommunicable components emerge and networks fail to synchronize. We show that the REBG method can effectively avoid the synchronization failure ($R=λ_{2}^{r}/λ_{N}^{r}=0$) which occurs in the residual degree gradient (RDG) method proposed in Phys. Rev. Lett. 103, 228702 (2009). Further experiments show that REBG method enhance synchronizability in networks with community structure as compared with the RDG method.

cond-mat.dis-nn↗

arXiv2010

Comment on "Dynamics and Directionality in Complex Networks"

Authors of Phys. Rev. Lett. 103, 228702 (2009) claim that "The residual degree gradient (RDG) method can enhance thesynchronizability of networks by simply changing the direction of the links". In this paper, we argue that in some case the RDG method will lead to the failure of synchronization ($R=λ^{r}_{2}/λ^{r}_{N}=0$). Additionally, we also propose a so-called residual betweenness gradient (RBG) method to solve this problem.

physics.soc-ph↗

arXiv2010

Dynamics on Spatial Networks and the Effect of Distance Coarse Graining

Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $δ$ in the power-law distance distribution for the average shortest path, traffic dynamics and navigation. Because the distance is estimated approximately in real world, we present an distance coarse graining procedure to generate the binary spatial networks in this paper. We find that the distance coarse graining procedure will result in the shifting of the optimal exponents $δ$. Interestingly, when the network is large enough, the effect of distance coarse graining can be ignored eventually. Additionally, we also study some main dynamic processes including traffic dynamics, navigation, synchronization and percolation on this spatial networks with coarse grained distance. The results lead us to the enhancement of spatial networks' specifical functions.

physics.soc-ph↗

arXiv2010

Emergence of Global Preferential Attachment From Local Interaction

Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this paper, it is found that the global preferential attachment emerges from the local interaction models, including distance-dependent preferential attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys. Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A. Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the attachment rate depends linearly on the degree or strength, while for acquaintance network model, the dependence follows a sublinear power law. It implies that for the evolution of social networks, local contact could be more fundamental than the presumed global preferential attachment. This is onsistent with the result observed in the evolution of empirical email networks.

cond-mat.stat-mech↗

arXiv2010

How to Measure Significance of Community Structure in Complex Networks

Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Recently, many approaches were proposed to community structure detection, but few works were focused on the significance of community structure. Since real networks obtained from complex systems always contain error links, and most of the community detection algorithms have random factors, evaluate the significance of community structure is important and urgent. In this paper, we use the eigenvectors' stability to characterize the significance of community structures. By employing the eigenvalues of Laplacian matrix of a given network, we can evaluate the significance of its community structure and obtain the optimal number of communities, which are always hard for community detection algorithms. We apply our method to many real networks. We find that significant community structures exist in many social networks and C.elegans neural network, and that less significant community structures appear in protein-interaction networks and metabolic networks. Our method can be applied to broad clustering problems in data mining due to its solid mathematical basis and efficiency.

physics.soc-ph↗

arXiv2010

Maximizing Entropy Yields Spatial Scaling in Social Networks

In addition to the well known common properties such as small world and community structures, recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $r$ scales as $P(r)\propto r^{-1}$. The basic principle that yields this spatial scaling property is not yet understood. Here we propose a fundamental origin for this law based on the concept of entropy. We show that this spatial scaling law can result from maximization of information entropy, which means individuals seek to maximize the diversity of their friendships. Such spatial distribution can benefit individuals significantly in optimally collecting information in a social network.

physics.soc-ph↗

arXiv2010

Effects of Levy Flights Mobility Pattern on Epidemic Spreading under Limited Energy Constraint

Recently, many empirical studies uncovered that animal foraging, migration and human traveling obey Levy flights with an exponent around -2. Inspired by the deluge of H1N1 this year, in this paper, the effects of Levy flights' mobility pattern on epidemic spreading is studied from a network perspective. We construct a spatial weighted network which possesses Levy flight spatial property under a restriction of total energy. The energy restriction is represented by the limitation of total travel distance within a certain time period of an individual. We find that the exponent -2 is the epidemic threshold of SIS spreading dynamics. Moreover, at the threshold the speed of epidemics spreading is highest. The results are helpful for the understanding of the effect of mobility pattern on epidemic spreading.

physics.soc-ph↗

arXiv2010

The attack tolerance of community structure in complex networks

Robustness is an important property of complex networks. Up to now, there are plentiful researches focusing on the network's robustness containing error and attack tolerance of network's connectivity and the shortest path. In this paper, the error and attack tolerance of network's community structure are studies through randomly and purposely disturbing interaction of networks. Two purposely perturbation methods are designed, that one methods is based on cluster coefficient and the other is attacking triangle. Dissimilarity function D is used to quantify the changes of community structure and modularity Q is used to quantify the significance of community structure. The numerical results show that after perturbation, network's community structure is damaged to be more unclear. It is also discovered that purposely attacking damages more to the community structure than randomly attacking.

cond-mat.stat-mech↗

arXiv2009

Unevenness of Loop Location in Complex Networks

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al find that real networks often have fewer short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.

physics.soc-ph↗

arXiv2009

Analyzing Netizen's View and Reply Behaviors on the Forum

Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. In this paper, we investigate the behavior of people on the $BBS$ forum by the statistical analysis of the amounts of view and reply of posts. According to our statistics, we find that the amounts of view and reply of posts follow the power law distributions with different power exponent. Furthermore, we discover that the amounts of view and reply of posts have nonlinear relationship. They are related by power function and show us straight line in log-log plot. Based on the estimation of slope and intercept of the line, we can characterize the behaviors quantitatively and know that people of Chinese forum and those of foreign forum have different preference towards replying to and viewing the posts. At last, we analyze the burstiness and memory in replying time series. They show some universal properties among different forum. All of them locate themselves in the high-$B$, low-$M$ region.

physics.soc-ph↗

arXiv2009

Scaling properties in spatial networks and its effects on topology and traffic dynamics

Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network's structure and function, a spatial network model is proposed. Based on a regular network and subject to a limited cost $C$, long range connections are added with power law distance distribution $P(r)=ar^{-δ}$. Some basic topological properties of the network with different $δ$ are studied. It is found that the network has the smallest average shortest path when $δ=2$. Then a traffic model on this network is investigated. It is found that the network with $δ=1.5$ is best for the traffic process. All of these results give us some deep understandings about the relationship between spatial structure and network function.

physics.soc-ph↗

arXiv2009

Optimal Tree for Both Synchronizability and Converging Time

It has been proved that the spanning tree from a given network has the optimal synchronizability, which means the index $R=λ_{N}/λ_{2}$ reaches the minimum 1. Although the optimal synchronizability is corresponding to the minimal critical overall coupling strength to reach synchronization, it does not guarantee a shorter converging time from disorder initial configuration to synchronized state. In this letter, we find that it is the depth of the tree that affects the converging time. In addition, we present a simple and universal way to get such an effective oriented tree in a given network to reduce the converging time significantly by minimizing the depth of the tree. The shortest spanning tree has both the maximal synchronizability and efficiency.

nlin.CD↗