一种可大范围调节聚类系数的加权无标度网络模型

在Barrat, Barthélemy 和 Vespignani (BBV)加权无标度网络模型的基础上，提出了一种可大范围调节聚类系数的加权无标度网络模型——广义BBV模型(GBBV模型).理论分析和仿真实验表明，GBBV模型保留了BBV模型的许多特征，节点度、节点权重和边权值等都服从幂律分布.但是，GBBV模型克服了BBV模型只能小范围调节聚类系数的缺陷，从而可以用于具有大聚类系数网络的建模. 关键词： 无标度网络 加权网络 聚类系数     

基于节点间依赖度的社团结构划分方法

本文提出了一种基于节点间依赖度的在复杂网络中划分社团结构的算法,定义了节点对其邻居的依赖度以及节点对社团的依赖度和条件依赖度.算法的基本要点是优先将最大依赖度不小于其他节点且有惟一依赖节点的节点划分到社团,并将对社团的依赖度或条件依赖度达到一定值的节点吸收进社团,直到所有节点都得到准确的社团划分.本算法在几个实际网络的测试上,都成功地划分出了满足条件的社团,并且对社团结构已知的网络的划分结果符合实际情况.     

一种能耗均衡的无线传感器网络加权无标度拓扑研究

针对无线传感器网络节点能耗不均衡问题,通过对节点生命期建模,得出节点生命期受节点剩余能量和通信距离的影响,进而将两端节点生命期作为构建拓扑时边权重的影响因子,通过边权重控制节点权重,最终得出了一种能耗均衡的无线传感器网络加权无标度拓扑模型,并理论证明了该模型的点权、边权和节点度均服从幂律分布.实验结果表明,该模型具有无标度拓扑的强容错性,并有效的均衡了网络中的节点能耗,延长了网络的生命期.     

基于簇相似度的网络社团结构探测算法

社团结构对复杂系统的结构特性和动力学特性有重要影响.提出了一个度量社团相似度的模型,称为簇相似度.该模型能够度量两个社团的相似度大小,为研究社团间的作用机制提供帮助.而且基于该模型,设计了一个社团划分算法.算法采用层次聚类的思想,每次合并两个相似度最大的社团,并通过一个评价函数选择最优社团划分.数值实验以及与CNM,GN,EigenMod等主流算法做比较,表明本算法的精度和效率都比较高,尤其对于边密度较高的网络,性能非常理想.     

多角度动态光散射加权贝叶斯反演算法

研究加权贝叶斯算法在多角度动态光散射法测量单峰分布颗粒体系的颗粒粒度分布中的应用.采用颗粒粒度信息分布为底数、调节参数为指数的权重系数给各个角度下的光强自相关函数曲线加入不同的权重系数，再利用传统的贝叶斯算法反演.模拟与实验结果表明，加权后的贝叶斯算法能获得分布误差更小的反演结果，有效地抑制了数据噪声的影响，提高颗粒粒度分布反演的准确性.     

激光时空混沌模型的加权网络投影同步

提出了一种实现加权网络时空混沌投影同步的方法.通过构造合适的Lyapunov函数,确定了加权网络中连接节点之间耦合函数的结构以及网络节点状态方程中分离配置的线性项的系数矩阵的取值范围.以Bragg声光双稳系统作为局域函数,单向耦合映像格子作为空间扩展系统构成激光时空混沌模型.通过仿真模拟检验了采用激光时空混沌模型作为网络节点的加权网络的投影同步效果.结果显示,对于任意的节点之间耦合强度的权重值,加权网络的投影同步均可以实现. 关键词： 投影同步 加权网络 时空混沌 Bragg声光双稳系统     

权重分布对加权网络效率的影响

加权网络可以对复杂系统的相互作用结构提供更加细致的刻画,而改变边权也成为调整和改善网络性质与功能的新途径.基于已有无权网络的效率概念,文中给出了相似权和相异权网络的网络效率定义,并研究了权重分布对于网络效率的影响.从平权的规则网络出发,通过改变权重的分布形式考察权重分布对网络效率的影响,结果发现,在规则网络上,权重分布随机性的增加提高了网络效率,而在几种常见的权重分布形式中,指数分布对网络效率的改进最为显著.同时,权重随机化之后网络最小生成树的总权重减小,意味着网络的运输成本随着权重异质性的增加而降低.以上结果为深入理解权重对网络结构与功能的影响提供了基础. 关键词： 复杂网络 加权网络 权重 网络效率     

一类高聚类系数的加权无标度网络及其同步能力分析

针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强. 关键词： 无标度网络 加权网络 聚类系数 同步能力     

基于联合矩阵分解的节点多属性网络社团检测

发现复杂网络中的社团结构在社会网络、生物组织网络和在线网络等复杂网络中具备十分重要的意义. 针对社交媒体网络的社团检测通常需要利用两种信息源: 网络拓扑结构特征和节点属性特征, 丰富的节点内容属性信息为社团检测的增加了灵活性和挑战. 传统方法是要么仅针对这两者信息之一进行单独挖掘, 或者将两者信息得到的社团结果进行线性叠加判决, 不能有效进行信息源的融合. 本文将节点的多维属性特征作为社团划分的一种有效协同学习项进行研究, 将两者信息源进行融合分析, 提出了一种基于联合矩阵分解的节点多属性网络社团检测算法CDJMF, 提高了社团检测的有效性和鲁棒性. 实验表明, 本文所提的方法能够有效利用节点的属性信息指导社团检测, 具备更高的社团划分质量.     

加权网络中基于冗余边过滤的k-核分解排序算法

k-核分解排序法对于度量复杂网络上重要节点的传播影响力具有重要的理论意义和应用价值,但其排序粗粒化的缺陷也不容忽视.最新研究发现,一些真实网络中存在局域连接稠密的特殊构型是导致上述问题的根本原因之一.当前的解决方法是利用边两端节点的外部连边数度量边的扩散性,采取过滤网络边来减少这种稠密结构给k-核分解过程造成的干扰,但这种方法并没有考虑现实网络上存在权重的普遍性.本文利用节点权重和权重分布重新定义边的扩散性,提出适用于加权网络结构的基于冗余边过滤的k-核分解排序算法:filter-core.通过世界贸易网、线虫脑细胞网和科学家合著网等真实网络的SIR(susceptible-infectedrecovered)传播模型的仿真结果表明,该算法相比其他加权k-核分解法,能够更准确地度量加权网络上具有重要传播影响力的核心节点及核心层.     

A weight’s agglomerative method for detecting communities in weighted networks based on weight’s similarity

This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge's weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes' functions effectively. In order to detect the community structure efficiently, a threshold coefficient κ to evaluate the equivalence of edges' weights and a new weighted modularity based on the weight's similarity are proposed. Then, constructing the weighted matrix and using the agglomerative mechanism, it presents a weight's agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes, the algorithm can detect the community structure in time O(n²log₂ⁿ). Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of κ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.     

The effect of weight on community structure of networks

The effect of weight on community structures is investigated in this paper. We use weighted modularity Q^w$Q^w$ to evaluate the partitions and weighted extremal optimization algorithm to detect communities. Starting from empirical and idealized weighted networks, the matching between weights and edges are disturbed. Then using similarity function S to measure the difference between community structures, it is found that the redistribution of weights does strongly affect the community structure especially in dense networks. This indicates that the community structure in networks is a suitable property to reflect the role of weight.     

Modelling of weighted evolving networks with community structures

Many social and biological networks consist of communities–groups of nodes within which links are dense but among which links are sparse. It turns out that most of these networks are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the link weights among their nodes. Recently, there are considerable interests in the study of properties as well as modelling of such networks with community structures. To our knowledge, however, no study of any weighted network model with such a community structure has been presented in the literature to date. In this paper, we propose a weighted evolving network model with a community structure. The new network model is based on the inner-community and inter-community preferential attachments and preferential strengthening mechanism. Simulation results indicate that this network model indeed reflect the intrinsic community structure, with various power-law distributions of the node degrees, link weights, and node strengths.     

Community detection with consideration of non-topological information

In a network described by a graph, only topological structure information is considered to determine how the nodes are connected by edges. Non-topological information denotes that which cannot be determined directly from topological information. This paper shows, by a simple example where scientists in three research groups and one external group form four communities, that in some real world networks non-topological information (in this example, the research group affiliation) dominates community division. If the information has some influence on the network topological structure, the question arises as to how to find a suitable algorithm to identify the communities based only on the network topology. We show that weighted Newman algorithm may be the best choice for this example. We believe that this idea is general for real-world complex networks.     

Refinement of the community detection performance by weighted relationship coupling

The complexity of many community detection algorithms is usually an exponential function with the scale which hard to uncover community structure with high speed. Inspired by the ideas of the famous modularity optimization, in this paper, we proposed a proper weighting scheme utilizing a novel k-strength relationship which naturally represents the coupling distance between two nodes. Community structure detection using a generalized weighted modularity measure is refined based on the weighted k-strength matrix. We apply our algorithm on both the famous benchmark network and the real networks. Theoretical analysis and experiments show that the weighted algorithm can uncover communities fast and accurately and can be easily extended to large-scale real networks.     

Properties of asymmetrically evolved community networks

This paper studies a simple asymmetrically evolved community network with a combination of preferential attachment and random properties. An important issue about community networks is to discover the different utility increments of two nodes, where the utility is introduced to investigate the asymmetrical effect of connecting two nodes. On the other hand, the connection of two nodes in community networks can be classified as two nodes belonging to the same or to different communities. The simulation results show that the model can reproduce a power-law utility distribution P(u)～u^-σ, σ = 2 + 1/p, which can be obtained by using mean-field approximation methods. Furthermore, the model exhibits exponential behaviour with respect to small values of a parameter denoting the random effect in our model at the low-utility region and a power-law feature with respect to big values of this parameter at the high-utility region, which is in good agreement with theoretical analysis. This kind of community network can reproduce a unique utility distribution by theoretical and numerical analysis.     

Detecting overlapping communities by seed community in weighted complex networks

Detection of community structures in the weighted complex networks is significant to understand the network structures and analysis of the network properties. We present a unique algorithm to detect overlapping communities in the weighted complex networks with considerable accuracy. For a given weighted network, all the seed communities are first extracted. Then to each seed community, more community members are absorbed using the absorbing degree function. In addition, our algorithm successfully finds common nodes between communities. The experiments using some real-world networks show that the performance of our algorithm is satisfactory.     

Recursive filtration method for detecting community structure in networks

Community detection is a topic of considerable recent interest within complex networks, but most methods proposed so far are divisive and agglomerative methods which delete only one edge each time to split the network, or agglomerating only one node each time until no individual node remains. Unlike those, we propose a method to split networks in parallel by deleting many edges in each filtration operation, and propose a community recursive coefficient (CRC) denoted by M instead of Q (modularity) to quantify the effect of the splitting results in this paper. We proved that recursive optimizing of the local M is equivalent to acquiring the maximal global Q value corresponding to good divisions. For a network with m edges, c communities and arbitrary topology, the method split the network at most c+1 times and detected the community structure in time O(m²+(c+1)m). We give several example applications, and show that the method can detect local communities according to the densities of external links to them in increasing order especially in large 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.     

Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit

In this paper, we propose a family of weighted extended Koch networks based on a class of extended Koch networks. They originate from a r-complete graph, and each node in each r-complete graph of current generation produces mr-complete graphs whose weighted edges are scaled by factor h in subsequent evolutionary step. We study the structural properties of these networks and random walks on them. In more detail, we calculate exactly the average weighted shortest path length (AWSP), average receiving time (ART) and average sending time (AST). Besides, the technique of resistor network is employed to uncover the relationship between ART and AST on networks with unit weight. In the infinite network order limit, the average weighted shortest path lengths stay bounded with growing network order (0 < h < 1). The closed form expression of ART shows that it exhibits a sub-linear dependence (0 < h < 1) or linear dependence (h = 1) on network order. On the contrary, the AST behaves super-linearly with the network order. Collectively, all the obtained results show that the efficiency of message transportation on weighted extended Koch networks has close relation to the network parameters h, m and r. All these findings could shed light on the structure and random walks of general weighted networks.