Effect of attachment strategies on bipartite networks

Bipartite systems show remarkable variations in their topological asymptotic properties,e.g., in their degree distribution. Such variations depend on the underlying growthdynamics. A scenario of particular importance is when the two partitions of the bipartitestructure do not grow at an equal rate. Here, we focus on the case where one of thepartitions can be assumed to be fixed while the other partition grows in time as observedin the codon-gene or alphabet-word network. We show that subtle changes in growthdynamics, particularly in the attachment kernel, can lead to drastic changes of theemergent topological properties. We present a detail analysis of various growthstrategies, including sequential and parallel addition of nodes, as well as with andwithout replacement attachment kernels. Analytical results have been compared withstochastic simulations as well as with real systems showing in all cases an excellentagreement.     

二分网上的靴襻渗流

靴襻渗流最早应用于统计物理学中研究磁铁因非磁性杂质导致磁有序的降低并最终消失的现象. 随着复杂网络研究的深入, 许多学者展开网络上的靴襻渗流研究. 在自然界中, 许多系统自然呈现出二分结构, 二分网络是复杂网络中的一种重要的网络模式. 本文通过建立动力学方程和计算机仿真模拟的方法研究二分网上的靴襻渗流, 关注的参数是二分网中两类节点初始的活跃比例和活跃阈值, 分别用f₁, f₂和Ω₁, Ω₂表示, 得到二分网两类节点终态活跃比例随初始活跃比例的变化会发生相变等结论. 同时 验证了动力学方程与仿真模拟的一致性.     

Percolation on bipartite scale-free networks

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 (kq)^−α, where α 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.     

在二部无标度网上的两性疾病传播

利用易感-感染-易感(SIS)传播模型研究人类性接触网上的病毒传播.当仅仅考虑异性性接触时,该网络是一个二部的无标度网.对这个网络上的SIS传播模型,通过率方程的方法分析了男性感染率和女性感染率与传染阈值之间的关系,发现女性感染者与男性感染者之比由网络的拓扑和男女感染率之比所确定.这一结果表明性接触网的拓扑对性传染病传播的重要性.最后给出了支持理论结果的数值模拟. 关键词： 性传染病 两性性接触网 无标度网络 二部图     

Effect of surface hydrogenation on the topological properties of multilayer graphene

We have investigated effects of surface hydrogenation on the topological properties of multilayer graphene by using density functional theory calculations and a tight-binding model. Hydrogen adsorption on a dimer site of a surface layer decouples the surface layer from the rest of the layers. Hydrogen adsorption on a nondimer site introduces a band mixing between the hydrogenated graphene and the rest of the graphene layers. The valley Hall effects and spin-valley-resolved Chern numbers of multilayer graphene, calculated as a function of the sublattice potential and the potential perpendicular to the layers, was found to be sensitive to details of inversion symmetry-breaking potentials. While the topological invariant depends on the adsorption site and spin polarization, surface-hydrogenated M-layer graphene was found to be topologically equivalent to (M-1)-layer graphene under inversion symmetry-breaking potentials regardless of the adsorption site.     

On the degree distribution of projected networks mapped from bipartite networks

Many real-world systems can be represented by bipartite networks. In a bipartite network, the nodes are divided into two disjoint sets, and the edges connect nodes that belong to different sets. Given a bipartite network (i.e. two-mode network) it is possible to construct two projected networks (i.e. one-mode networks) where each one is composed of only one set of nodes. While network analyses have focused on unipartite networks, considerably less attention has been paid to the analytical study of bipartite networks. Here, we analytically derive simple mathematical relationships that predict degree distributions of the projected networks by only knowing the structure of the original bipartite network. These analytical results are confirmed by computational simulations using artificial and real-world bipartite networks from a variety of biological and social systems. These findings offer in our view new insights into the structure of real-world bipartite networks.     

Effect of edge removal on topological and functional robustness of complex networks

We study the robustness of several network models subject to edge removal. The robustness is measured by the statistics of network breakdowns, where a breakdown is defined as the destroying of the total connectedness of a network, rather than the disappearance of the giant component. We introduce a simple traffic dynamics as the function of a network topology, and the total connectedness can be destroyed in the sense of either the topology or the function. The overall effect of the topological breakdown and the functional breakdown, as well as the relative importance of the topological robustness and the functional robustness, are studied under two edge removal strategies.     

Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network sampling. Therefore, it becomes critical to devise effective means for sound estimation of network topological and dynamical properties while avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential is illustrated with respect to two real-world networks, namely bone canals and air transportation.     

An evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike  , show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p$p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p$p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.     

Personal recommendation via unequal resource allocation on bipartite networks

In this paper, we present a recommendation algorithm based on the resource-allocation progresses on bipartite networks. In this model, each node is assigned an attraction that is proportional to the power of its degree, where the exponent β is an adjustable parameter that controls the configuration of attractions. In the resource-allocation process, each transmitter distributes its each neighbor a fragment of resource that is proportional to the attraction of the neighbor. Based on a benchmark database, we find that decreasing the attractions that the nodes with higher degrees are assigned can further improve the algorithmic accuracy. More significantly, numerical results show that the optimal configuration of attractions subject to accuracy can also generate more diverse and less popular recommendations.     

Effects of high-order correlations on personalized recommendations for bipartite networks

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user-user correlations are obtained by a diffusion process. Furthermore, by considering the second-order correlations, we design an effective algorithm that depresses the influence of mainstream preferences. Simulation results show that the algorithmic accuracy, measured by the average ranking score, is further improved by 20.45% and 33.25% in the optimal cases of MovieLens and Netflix data. More importantly, the optimal value depends approximately monotonously on the sparsity of the training set. Given a real system, we could estimate the optimal parameter according to the data sparsity, which makes this algorithm easy to be applied. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that as the sparsity increases, the algorithm considering the second-order correlation can outperform the MCF simultaneously in all three criteria.     

Abe homotopy classification of topological excitations under the topological influence of vortices

Topological excitations are usually classified by the nth homotopy group πn. However, for topological excitations that coexist with vortices, there are cases in which an element of πn cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of πn corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π₁ on πn. In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κn. The nth Abe homotopy group κn is defined as a semi-direct product of π₁ and πn. In this framework, the action of π₁ on πn is understood as originating from noncommutativity between π₁ and πn. We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is Sn/K, where Sn is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).     

Features of the electronic spectrum of alloys with electronic topological transition and their influence on physical properties

Occurrence of a discrete spectrum of electrons of small groups as result of the electronic topological transition in Mo-Re alloys is expected on the basis of the experimental results. Such a spectrum arises against the background of the continuous spectrum of electrons of large groups and corresponds to partial localization of electrons.     

Clustering coefficient and community structure of bipartite networks

Many real-world networks display natural bipartite structure, where the basic cycle is a square. In this paper, with the similar consideration of standard clustering coefficient in binary networks, a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed. In order to detect community structures in bipartite networks, two different edge clustering coefficients LC₄ and LC₃ of bipartite networks are defined, which are based on squares and triples respectively. With the algorithm of cutting the edge with the least clustering coefficient, communities in artificial and real world networks are identified. The results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks.     

Identifying missing and spurious connections via the bi-directional diffusion on bipartite networks

Link prediction and spurious link detection in complex networks have attracted increasing attention from both physical and computer science communities, due to their wide applications in many real systems. Related previous works mainly focus on monopartite networks while these problems in bipartite networks are not yet systematically addressed. Containing two different kinds of nodes, bipartite networks are essentially different from monopartite networks, especially in node similarity calculation: the similarity between nodes of different kinds (called inter-similarity) is not well defined. In this letter, we employ the local diffusion processes to measure the inter-similarity in bipartite networks. We find that the inter-similarity is asymmetric if the diffusion is applied in different directions. Accordingly, we propose a bi-directional hybrid diffusion method which is shown to achieve higher accuracy than the existing diffusion methods in identifying missing and spurious links in bipartite networks.     

基于二分图的温度网络拓扑性质研究

利用中国地区435个台站1961—2002年逐日平均温度序列,将温度变化发生在9天时间尺度上的特征编码在网络中,通过研究二分图温度网络(BGT网络)中节点与项目的关系,揭示出9天时间尺度上温度变化的特征及其在空间上的拓扑统计性质.网络中各节点RRRD, RrDD, eeed, DRRD, DDRR等所代表的温度波动模态在网络中异常频发,对9天尺度温度变化的预报有一定的指导意义.统计网络的节点度分布,集群系数等拓扑结构特征量,发现BGT网络服从正态分布特征.BGT网络项目内节点度的多样性大体上 关键词： 二分图温度网络 气候系统 拓扑结构     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

社交网络中基于贝叶斯和半环代数模型的节点影响力计算机理

本文综合考虑网络结构及节点间的互动等关键因素, 提出了一种节点影响力分布式计算机理. 首先根据节点交互行为在时域上的自相似特性, 运用带折扣因子的贝叶斯模型计算节点间的直接影响力; 然后运用半环模型来分析节点间接影响力的聚合; 最后根据社交网络的小世界性质及传播门限, 综上计算出节点的综合影响力. 仿真结果表明, 本文给出的模型能有效抑制虚假粉丝导致的节点影响力波动, 消除了虚假粉丝的出现对节点影响力计算带来的干扰, 从中选择影响力高的若干节点作为传播源节点, 可以将信息传播到更多数目的节点, 促进了信息在社交网络中的传播. 关键词： 社交网络 影响力 贝叶斯 半环代数     

拓扑缺陷对Armchair型小管径多壁碳纳米管输运性质的影响

采用密度泛函理论和非平衡格林函数方法研究了纯净的及带有不同数目的Stone-Wale拓扑缺陷下的扶手椅型单壁, 双壁和三壁小管径碳纳米管的能带结构和电子输运性质, 通过计算并分析不同偏压下的微分电导和非弹性电子隧穿谱(IETS), 计算结果表明单壁, 双壁和三壁碳纳米管的特征偏压区间分别为[-1.0V, 1.0V], [-0.5V, 0.5V] 和[-0.25V, 0.25V], 特征偏压区间内SW拓扑缺陷所产生的电导波动平缓, 而特征偏压区间外因缺陷的数目变化所带来的电导波动显著, 通过IETS谱线的分析得到单壁, 双壁和三壁碳纳米管的特征峰偏压分别为 1.25V, 0.625V和 0.125V. 碳纳米管的特征偏压区间和IETS特征峰偏压可为较小管径碳纳米管单壁, 双壁和多壁类型的区分提供一种新的途径, 同时也为小管径多壁碳纳米管的输运性质在出现拓扑缺陷时的响应提供参考依据.