Spatially Extended Networks with Singular Multi-scale Connectivity Patterns

The cortex is a very large network characterized by a complex connectivity including at least two scales: a microscopic scale at which the interconnections are non-specific and very dense, while macroscopic connectivity patterns connecting different regions of the brain at larger scale are extremely sparse. This motivates to analyze the behavior of networks with multiscale coupling, in which a neuron is connected to its \(v(N)\) nearest-neighbors where \(v(N)=o(N)\) , and in which the probability of macroscopic connection between two neurons vanishes. These are called singular multi-scale connectivity patterns. We introduce a class of such networks and derive their continuum limit. We show convergence in law and propagation of chaos in the thermodynamic limit. The limit equation obtained is an intricate non-local McKean–Vlasov equation with delays which is universal with respect to the type of micro-circuits and macro-circuits involved.     

The randomly organized structure of urban ground bus-transport networks in China

In this paper, the evolution dynamical properties of four topological urban ground bus-transport networks (BTNs) in China are empirically researched. As the statistical results of some common used measurements show that there are large fluctuations because of small sample sizes to induce some indistinct conclusions, and there are even incorrect BTN structure pictures as positive degree relation of the adjacent vertices in those BTNs though they are actually uncorrelated at all, i.e., exhibiting “pseudo positive connectivity correction”. Thus in order to uncover the randomly organized architecture of BTNs, new measurements of the average sum of the nearest-neighbors’ degree-degree correlation D_nn(k), and the degree average edges among the nearest-neighbors L(k) are proposed. The obtained results of two new measurements do reflect that the considered BTNs are organized randomly. In this point, those empirical results provide one new framework for a more realistic BTN model, which will capture the underlying evolution principles of a BTN in the geographical topology.     

相依网络上基于相连边的择优恢复算法

如何有效地应对和控制故障在相依网络上的级联扩散避免系统发生结构性破碎,对于相依网络抗毁性研究具有十分重要的理论价值和现实意义.最新的研究提出一种基于相依网络的恢复模型,该模型的基本思想是通过定义共同边界节点,在每轮恢复阶段找出符合条件的共同边界节点并以一定比例实施恢复.当前的做法是按照随机概率进行选择.这种方法虽然简单直观,却没有考虑现实世界中资源成本的有限性和择优恢复的必然性.为此,针对相依网络的恢复模型,本文利用共同边界节点在极大连通网络内外的连接边数计算边界节点的重要性,提出一种基于相连边的择优恢复算法(preferential recovery based on connectivity link,PRCL)算法.利用渗流理论的随机故障模型,通过ER随机网络和无标度网络构建的不同结构相依网络上的级联仿真结果表明,相比随机方法和度数优先以及局域影响力优先的恢复算法,PRCL算法具备恢复能力强、起效时间早且迭代步数少的优势,能够更有效、更及时地遏制故障在网络间的级联扩散,极大地提高了相依网络遭受随机故障时的恢复能力.     

基于Web 2.0的边与节点同时增长网络模型

模拟了Web2.0网络的发展过程并研究其拓扑结构,分析某门户网站实际博客数据的度分布、节点度时间变化,发现与先前的无标度网络模型有所差别.根据真实网络的生长特点,提出了边与节点同时增长的网络模型,包括随机连接及近邻互联的网络构造规则.仿真研究表明,模拟的网络更接近实际,在没有优先连接过程时,模型能得到幂率的度分布;并且网络有更大的聚类系数以及正的度相关性。     

A Resiliency-Connectivity metric in wireless sensor networks with key predistribution schemes and node compromise attacks

Applications for wireless sensor networks require widespread, highly reliable communications even in the face of adversarial influences. Maintaining connectivity and secure communications between entities are vital networking properties towards ensuring the successful and accurate completion of desired sensing tasks. We examine the required communication range for nodes in a wireless sensor network with respect to several parameters. Network properties such as key predistribution schemes and node compromise attacks are modelled with several network parameters and studied in terms of how they influence global network connectivity. These networks are physically vulnerable to malicious behavior by way of node compromise attacks that may affect global connectivity. We introduce a metric that determines the resilience of a network employing a key predistribution scheme with respect to node compromise attacks. In this work,we provide the first study of global network connectivity and its relationship to node compromise attacks. Existing work considers the relationship between the probability of node compromise and the probability of link compromise and the relationship of the probability of secure link establishment and overall network connectivity for the Erdős network model. Here, we present novel work which combines these two relationships to study the relationship between node compromise attacks and global network connectivity. Our analysis is performed with regard to large-scale networks; however, we provide simulation results for both large-scale and small-scale networks. First, we derive a single expression to determine the required communication radius for wireless sensor networks to include the effects of key predistribution schemes. From this, we derive an expression for determining required communication range after an adversary has compromised a fraction of the nodes in the network. The required communication range represents the resource usage of nodes in a network to cope with key distribution schemes and node compromise attacks. We introduce the Resiliency-Connectivity metric, which measures the resilience of a network in expending its resources to provide global connectivity in adverse situations.     

Scale-free networks from varying vertex intrinsic fitness

A new mechanism leading to scale-free networks is proposed in this Letter. It is shown that, in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Assigning a quenched fitness value x(i) to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a good-get-richer mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected).     

Synchronization optimal networks obtained using local structure information

In this paper, the networks with optimal synchronizability are obtained using the local structure information. In scale-free networks, a node will be coupled by its neighbors with maximal degree among the neighbors if and only if the maximal degree is larger than its own degree. If the obtained coupled networks are connected, they are synchronization optimal networks. The connection probability of coupled networks is greatly affected by the average degree which usually increases with the average degree. This method could be further generalized by taking into account the degree of next-nearest neighbors, which will sharply increase the connection probability. Compared to the other proposed methods that obtain synchronization optimal networks, our method uses only local structure information and can hold the structure properties of the original scale-free networks to some extent. Our method may present a useful way to manipulate the synchronizability of real-world scale-free networks.     

Hierarchical Characterization of Complex Networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.     

Prisoner's Dilemma Game on Two Types of Positively Correlated Networks

We study the effects of degree correlations on the evolution of cooperation in the prisoner＇s dilemma game with individuals located on two types of positively correlated networks. It is shown that the positive degree correlation can either promote or inhibit the emergence of cooperation depending on network configurations. Furthermore, we investigate the probability to cooperate as a function of connectivity degree, and find that high-degree individuals generally have a higher tendency to cooperate. Finally, it is found that small-degree individuals usually change their strategy more frequently, and such change is shown to be unfavourable to cooperation for both kinds of networks.     

Weighted and unweighted network of amino acids within protein

The information regarding the structure of a single protein is encoded in the network of interacting amino acids considered as nodes. If any two atoms from two different amino acids (nodes) are within higher cut-off distance of London-van der Waals forces, the amino acids are considered to be linked or connected. Several atoms of any amino acids in a protein may be within the above prescribed distance of several atoms of another amino acid resulting in possible multiple links between them. These multiple links are the basis of the weight of the connectivity in a protein network. Each protein has been considered as a weighted and an unweighted network of amino acids. A total of forty nine protein structures that covers the three branches of life on earth has been analyzed and several network properties have been studied. The probability degree and strength distributions of network connectivity have been obtained. It has been observed that the average strength of amino acid node depends on its degree. The results show that the average clustering coefficient of weighted network is less than that of unweighted network. It implies that the topological clustering is generated by edges with low weights. The power-law behavior of clustering coefficients of weighted and unweighted networks as a function of degree indicates that they have signatures of hierarchy. It has also been observed that the network is of assortative type.     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.     

Structure properties and synchronizability of cobweb-like networks

The cobweb-like network was constructed, and its structure properties and synchronizability were studied by numerical simulation and probability theory. For cobweb-like networks, the behaviors of structure properties with the adding probability are similar to those for the small-world network. However, the properties of cobweb-like networks also distinctly depend on the spoke-ring ratio r. With increasing r, the average path length decreases, and the average clustering coefficient increases. Simultaneously, the connectivity distribution becomes heterogeneous. Moreover, in the case of bounded synchronized region, the synchronizability shows complicated behaviors with r, and is enhanced favorably at r=2.28 with homogeneous load distribution. The reason is that homogeneous load distribution has an advantage over the communication between oscillators, which efficiently leads to global synchronization. This work could be useful for design and kinetic property research of cobweb-like networks.     

Continuous-time quantum walks on Erdös-Rényi networks

We study the coherent exciton transport of continuous-time quantum walks (CTQWs) on Erdös-Rényi networks. We numerically investigate the transition probability between two nodes of the networks, and compare the classical and quantum transport efficiency on networks of different connectivity. In the long time limiting, we find that there is a high probability to find the exciton at the initial node. We also study how the network parameters affect such high return probability.     

Detection of influential nodes with multi-scale information

The identification of influential nodes in complex networks is one of the most exciting topics in network science. The latest work successfully compares each node using local connectivity and weak tie theory from a new perspective. We study the structural properties of networks in depth and extend this successful node evaluation from single-scale to multi-scale. In particular, one novel position parameter based on node transmission efficiency is proposed, which mainly depends on the shortest distances from target nodes to high-degree nodes. In this regard, the novel multi-scale information importance (MSII) method is proposed to better identify the crucial nodes by combining the network's local connectivity and global position information. In simulation comparisons, five state-of-the-art algorithms, i.e. the neighbor nodes degree algorithm (NND), betweenness centrality, closeness centrality, Katz centrality and the k-shell decomposition method, are selected to compare with our MSII. The results demonstrate that our method obtains superior performance in terms of robustness and spreading propagation for both real-world and artificial networks.     

Maximum entropy networks are more controllable than preferential attachment networks

A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution.     

The physical position neighbourhood evolving network model

Many social, technological, biological and economical systems are properly described by evolved network models. In this paper, a new evolving network model with the concept of physical position neighbourhood connectivity is proposed and studied. This concept exists in many real complex networks such as communication networks. The simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of the graph Laplacian, clustering coefficients, average distances and degree distributions for different evolving parameters of this model are presented. The dynamical behaviour of each node on the consensus problem is also studied. It is found that the degree distribution of this new model represents a transition between power-law and exponential scaling, while the Barábasi-Albert scale-free model is only one of its special (limiting) cases. It is also found that the time to reach a consensus becomes shorter sharply with increasing of neighbourhood scale of the nodes.     

Local affinity in heterogeneous growing networks

In this paper we present a study of the influence of local affinity in heterogeneous preferential attachment (PA) networks. Heterogeneous PA models are a generalization of the Barabási-Albert model to heterogeneous networks, where the affinity between nodes biases the attachment probability of links. Threshold models are a class of heterogeneous PA models where the affinity between nodes is inversely related to the distance between their states. We propose a generalization of threshold models where network nodes have individual affinity functions, which are then combined to yield the affinity of each potential interaction. We analyze the influence of the affinity functions in the topological properties averaged over a network ensemble. The network topology is evaluated through the distributions of connectivity degrees, clustering coefficients and geodesic distances. We show that the relaxation of the criterion of a single global affinity still leads to a reasonable power-law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions. We also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks.     

Emergence of modularity and disassortativity in protein-protein interaction networks

In this paper, we present a simple evolution model of protein-protein interaction networks by introducing a rule of small-preference duplication of a node, meaning that the probability of a node chosen to duplicate is inversely proportional to its degree, and subsequent divergence plus nonuniform heterodimerization based on some plausible mechanisms in biology. We show that our model cannot only reproduce scale-free connectivity and small-world pattern, but also exhibit hierarchical modularity and disassortativity. After comparing the features of our model with those of real protein-protein interaction networks, we believe that our model can provide relevant insights into the mechanism underlying the evolution of protein-protein interaction networks.     

Age-based model for weighted network with general assortative mixing

In this paper, we propose an evolutionary model for weighted networks by introducing an age-based mutual selection mechanism. Our model generates power-law distributions of degree, weight, and strength, which are confirmed by analytical predictions and are consistent with real observations. The investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks. Furthermore, both assortative and disassortative properties can be naturally obtained by tuning a parameter α, which controls the strength of age-based preferential attachments. Since the age information of nodes is easier to acquire than the degree and strength of nodes, and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation, our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks.