复杂社会网络的介数性质近似计算方法研究

随着计算机和互联网的迅猛发展,面向互联网的社会网络挖掘和分析成为一个新的课题。从互联网挖掘的社会网络往往规模巨大,这对网络分析算法的性能提出了更高的要求 。介数值作为图的重要结构性质,广泛应用于基于图的聚类、分类算法,如何降低其计算的复杂性是急需解决的问题。目前,常用的方法是利用对最短路径长度的近似来降低低网络分析算法的复杂性,但已有的近似方法没有考虑现实大规模网络的复杂网络特性,对最短路径长度的近似方 近似计算方法,其基本思想是结合复杂网络的结构特性,利用通过网络中枢节点的路径来近似最短路径,以近似的最短路径求得介数的近似值。这为图的结构性质的近似估算算提供了一种新颖的思路。通过与传统的介数计算方法和近的分析得到了若干有益的结论,为进一步的研究工作奠定了基础。     

基于介中心性及K-shell的脑网络核心节点评价方法

在对基于核磁共振成像技术重构得到的人脑结构网络的研究中,核心节点的识别是对全脑网络特性展开研究的基础,具有重要意义。给出了一种基于K-shell和介中心性的核心节点评价方法,首先使用以节点局部重要性为标准的度中心性、邻近中心性和介中心性三个中心性评价方法分别对人脑结构网络中的节点重要性展开评估和分析;接着利用以节点全局地位为标准的K-shell分解法对人脑结构网络的核心节点展开分析。实验结果显示,由于同时兼顾了脑网络节点的整体特性和局部特性,该方法能够更全面和准确地识别核心脑区节点。     

一种基于最短路径介数的重要节点发现算法

网络中重要节点的发现是研究网络特性的重要方面之一,在复杂网络、系统科学、社会网分析和互联网搜索等领域中具有广泛的应用价值。为提高全网范围内重要节点发现的效率和有效性,提出了一种基于最短路径介数及节点中心接近度的重要节点发现算法,通过最短路径介数的方法确定全网内的重要节点,利用中心接近度分析重要节点的重要性。测试结果表明,与同类的系统比较起来,该方法具有比较好的性能。     

基于中介中心度的微博影响力个体发现

微博中重要影响力个体的发现有着极为重要的作用。中介中心度方法是发现网络中重要节点的有效方法, 然而传统的中介中心度方法只适用于小规模的网络, 对于海量的微博网络信息却无能为力。提出一种基于随机游走的中介中心度算法, 该算法不仅能有效地应对海量的微博网络数据, 而且其发现结果也明显优于相关的研究。     

Optimal Controlled Nodes Selection for Fast Consensus

Motivated by the significance of optimizing network performance with limited resources in real applications, we investigate the problem of achieving fast and desired consensus in a complex network via pinning control a fraction of nodes in the network. An optimization problem is proposed to select p optimal pinned nodes to guarantee fastest consensus, which is relaxed to a Mixed‐Integer Semi‐Definite Program. In the single pinned node case (i.e., p = 1), we find that the optimal pinned node is the node with highest min‐max distance centrality within the nodes with highest closeness centrality in the network. In the multiple pinned nodes case (i.e., p > 1), we find that betweenness centrality could be used as a suboptimal index to select pinned nodes.     

基于社区的动态网络节点介数中心度更新算法

随着互联网技术的迅猛发展,社会网络呈现出爆炸增长的趋势,传统的静态网络分析方法越来越难以达到令人满意的效果,于是对网络进行动态分析就成为社会网数据管理领域的一个研究热点。节点介数中心度衡量的是一个节点对图中其他点对最短路径的控制能力,有利于挖掘社会网络中的重要节点。在图结构频繁变化的场合,若每次变化后都重新计算整个图中所有节点的介数中心度,则效率将会很低。针对动态网络中节点介数中心度计算困难的问题,本文提出一种基于社区的节点介数中心度更新算法。通过维护社区与社区、社区与节点的最短距离集合,快速过滤掉那些在网络动态更新中不受影响的点对,从而大大提高节点介数中心度的更新效率。真实数据集和合成数据集上的实验结果表明了论文所提算法的有效性。     

Estimating graph distance and centrality on shared nothing architectures

We present a parallel toolkit for pairwise distance computation in massive networks. Computing the exact shortest paths between a large number of vertices is a costly operation, and serial algorithms are not practical for billion‐scale graphs. We first describe an efficient parallel method to solve the single source shortest path problem on commodity hardware with no shared memory. Using it as a building block, we introduce a new parallel algorithm to estimate the shortest paths between arbitrary pairs of vertices. Our method exploits data locality, produces highly accurate results, and allows batch computation of shortest paths with 7% average error in graphs that contain billions of edges. The proposed algorithm is up to two orders of magnitude faster than previously suggested algorithms and does not require large amounts of memory or expensive high‐end servers. We further leverage this method to estimate the closeness and betweenness centrality metrics, which involve systems challenges dealing with indexing, joining, and comparing large datasets efficiently. In one experiment, we mined a real‐world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20‐node commodity cluster. Copyright © 2014 John Wiley & Sons, Ltd.     

基于复杂网络分析的软件高危缺陷评估方法

为了评估软件缺陷的风险,提出了一种基于复杂网络分析的软件缺陷评估方法。该方法首先用一个网络模型表达程序实体之间的关系,将源代码中的方法抽象为节点,方法间的调用关系抽象为有向边,以此构造程序源代码网络;然后分别用介数算法和PageRank算法计算造成软件缺陷的方法节点在源代码全局网络中的地位,由此评估缺陷的风险高低。实验结果表明,该方法在评估内部高危缺陷时有较好的效果,有助于提高软件开发维护人员对一些隐蔽高危缺陷的关注度,进而为后续修复缺陷与软件演化提供有益的线索。     

Second order centrality: Distributed assessment of nodes criticity in complex networks

A complex network can be modeled as a graph representing the “who knows who” relationship. In the context of graph theory for social networks, the notion of centrality is used to assess the relative importance of nodes in a given network topology. For example, in a network composed of large dense clusters connected through only a few links, the nodes involved in those links are particularly critical as far as the network survivability is concerned. This may also impact any application running on top of it. Such information can be exploited for various topological maintenance issues to prevent congestion and disruption. This can also be used offline to identify the most important actors in large social interaction graphs. Several forms of centrality have been proposed so far. Yet, they suffer from imperfections: initially designed for small social graphs, they are either of limited use (degree centrality), either incompatible in a distributed setting (e.g. random walk betweenness centrality).In this paper we introduce a novel form of centrality: the second order centrality which can be computed in a distributed manner. This provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion. To this end, each node records the time elapsed between visits of that random walk (called return time in the sequel) and computes the standard deviation (or second order moment) of such return times. The key point is that central nodes see regularly the random walk compared to other topology nodes. Both through theoretical analysis and simulation, we show that the standard deviation can be used to accurately identify critical nodes as well as to globally characterize graphs topology in a distributed way. We finally compare our proposal to well-known centralities to assess its competitivity.     

Robust network planning in nonuniform traffic scenarios

Robustness to the environmental variations is an important feature of any reliable communication network. This paper reports on a network theory approach to the design of such networks where the environmental changes are traffic fluctuations, topology modifications, and changes in the source of external traffic. Motivated by the definition of betweenness centrality in network science, we introduce the notion of traffic-aware betweenness (TAB) for data networks, where usually an explicit (or implicit) traffic matrix governs the distribution of external traffic into the network. We use the average normalized traffic-aware betweenness, which is referred to as traffic-aware network criticality (TANC), as our main metric to quantify the robustness of a network. We show that TANC is directly related to some important network performance metrics, such as average network utilization and average network cost. We prove that TANC is a linear function of end-to-end effective resistances of the graph. As a result, TANC is a convex function of link weights and can be minimized using convex optimization techniques. We use semi-definite programming method to study the properties of the optimization problem and derive useful results to be employed for robust network planning purposes.     

一个基于中心度的社团结构发现新算法*

针对GN算法在社团结构发现中时间复杂度高等问题,提出一种基于中心度的GN改进算法（DCGN）。该算法根据节点中心度以及节点之间的最短路径首先确定社团结构中心节点集,然后逐步删除社团结构中心节点之间的最大边介数连边,完成社团结构划分。DCGN算法避免了GN算法边介数计算开销大的问题,算法的时间复杂度约为O(cmn),其中c为常数,n为网络成员数,m为网络连边数。将DCGN和GN算法同时应用到Zachary网络及计算机随机生成网络中并进行了比较。实验结果表明,所提出的DCGN算法在运行效率和效果方面较之GN算     

Centralities of a network and its line graph: an analytical comparison by means of their irregularity

Given a network G, it is known that the Bonacich centrality of the bipartite graph B(G) associated with G can be obtained in terms of the centralities of the line graph L(G) associated with G and the centrality of the network G+gr (whose adjacency matrix is obtained by adding to the adjacency matrix A(G) the diagonal matrix D=b_ij, where b_ii is the degree of node i in G) and conversely. In this contribution, we use the centrality of G to estimate the centrality of G+gr and show that the error committed is bounded by some measure of the irregularity of G. This estimate gives an analytical comparison of the eigenvector centrality of G with the centrality of L(G) in terms of some irregularity measure of G.     

Semi-supervised classification and betweenness computation on large, sparse, directed graphs

This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1] and [2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85% classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation.     

A methodology for the characterization of flow conductivity through the identification of communities in samples of fractured rocks

We present a methodology that characterizes through the topology of a network the capability of flow conductivity in fractures associated to a reservoir under study. This strategy considers the fracture image as a graph, and is focused on two key aspects. The first is to identify communities or sets of nodes that are more conductive, and the second one is to find nodes that form the largest paths and have therefore more possibility of serving as flow channels. The methodology is divided into two stages, the first stage obtains the cross points from fracture networks. The second stage deepens on the community identification. This second stage carries out the process of identifying conductive nodes by using centrality measures (betweenness, eccentricity and closeness) for evaluating each node in the network. Then an optimization modularity method is applied in order to form communities using two different types of weights between cross points or nodes. Finally, each community is associated with the average value of each measure. In this way the maximum values in betweenness and eccentricity are selected for identifying communities with the most important nodes in the network. The results obtained allow us to show regions in the fracture network that are more conductive according to the topology. In addition, this general methodology can be applied to other fracture characteristics.     

复杂网络中的一种介度熵抗毁性度量方法

在复杂网络中，核心节点的损坏可能会影响到整个网络的稳定性。基于节点重要性研究了网络抗毁性度量和抗毁性能。综合考虑节点度值和介数对节点重要性的影响，提出了局部介-度中心性指标。兼顾节点的聚集系数，提出节点抗毁性度量方法。为了估量网络的抗毁性能，提出了介-度熵度量及其算法。仿真攻击实验结果表明，基于介-度中心性的攻击策略移除约20%的节点后，可将网络近似地分割为孤立节点集合，它优于传统的攻击策略，表明介-度中心性指标可以更准确地刻画节点重要性。对不同模拟网络的抗毁性评估计算结果则表明，介-度熵度量对网络抗毁性能的排序符合实际情况，在衡量网络抗毁性方面是完全合理的。     

EDGly: detection of influential nodes using game theory

Identifying those nodes that play a critical role within a network is of great importance. Many applications such as gossip spreading, disease spreading, news dispersion, identifying prominent individuals in a social network, etc. may take advantage of this knowledge in a complex network. The basic concept is generally to identify the nodes with the highest criticality in a network. As a result, the centrality principle has been studied extensively and in great detail, focusing on creating a consistent and accurate location of nodes within a network in terms of their importance. Both single centrality measures and group centrality measures, although, have their certain drawbacks. Other solutions to this problem include the game-theoretic Shapley Value (SV) calculations measuring the effect of a collection of nodes in complex networks via dynamic network data propagation process. Our novel proposed algorithm aims to find the most significant communities in a graph with community structure and then employs the SV-based games to find the most influential node from each community. A Susceptible-Infected-Recovered (SIR) model has been employed to distinctly determine each powerful node's capacity to spread. The results of the SIR simulation have also been used to show the contrast between the spreading capacity of nodes found through our proposed algorithm and that of nodes found using SV-algorithm and centrality measures alone.

     

面向Web文本关键词自动抽取的DON模型研究

Web网页中往往包含许多主题噪声,准确地自动抽取关键词成为技术难点。提出了一个文本对象网络模型DON,给出了对象节点的中心度概念和基于中心度的影响因子传播规则,并据此自动聚集DON中的主题社区（topic society）,从而提高了模型的抗噪能力。提出一个基于DON的网页关键词自动抽取算法KEYDON（Keywords Extraction Algorithm Based on DON）。实验结果表明,与基于DocView模型的相应算法相比,KEYDON的准确率提高了近20%,这说明DON模型具有较强的抑制主题噪声能力。     

Using core-periphery structure to predict high centrality nodes in time-varying networks

Vertices with high betweenness and closeness centrality represent influential entities in a network. An important problem for time varying networks is to know a-priori, using minimal computation, whether the influential vertices of the current time step will retain their high centrality, in the future time steps, as the network evolves. In this paper, based on empirical evidences from several large real world time varying networks, we discover a certain class of networks where the highly central vertices are part of the innermost core of the network and this property is maintained over time. As a key contribution of this work, we propose novel heuristics to identify these networks in an optimal fashion and also develop a two-step algorithm for predicting high centrality vertices. Consequently, we show for the first time that for such networks, expensive shortest path computations in each time step as the network changes can be completely avoided; instead we can use time series models (e.g., ARIMA as used here) to predict the overlap between the high centrality vertices in the current time step to the ones in the future time steps. Moreover, once the new network is available in time, we can find the high centrality vertices in the top core simply based on their high degree. To measure the effectiveness of our framework, we perform prediction task on a large set of diverse time-varying networks. We obtain F1-scores as high as 0.81 and 0.72 in predicting the top m closeness and betweenness centrality vertices respectively for real networks where the highly central vertices mostly reside in the innermost core. For synthetic networks that conform to this property we achieve F1-scores of 0.94 and 0.92 for closeness and betweenness respectively. We validate our results by showing that the practical effects of our predicted vertices match the effects of the actual high centrality vertices. Finally, we also provide a formal sketch demonstrating why our method works.     

Discovering and tracking query oriented active online social groups in dynamic information network

The efficient identification of social groups with common interests is a key consideration for viral marketing in online social networking platforms. Most existing studies in social groups or community detection either focus on the common attributes of the nodes (users) or rely on only the topological links of the social network graph. The temporal evolution of user activities and interests have not been thoroughly studied to identify their effects on the formation of groups. In this paper, we investigate the problem of discovering and tracking time-sensitive activity driven user groups in dynamic social networks for a given input query consisting a set of topics. The users in these groups have the tendency to be temporally similar in terms of their activities on the topics of interest. To this end, we develop two baseline solutions to discover effective social groups. The first solution uses the network structure, whereas the second one uses the topics of common interest. We further propose an index-based method to incrementally track the evolution of groups with a lower computational cost. Our main idea is based on the observation that the degree of user activeness often degrades or upgrades widely over a period of time. The temporal tendency of user activities is modelled as the freshness of recent activities by tracking the social streams with a fading time window. We conduct extensive experiments on three real data sets to demonstrate the effectiveness and efficiency of the proposed methods. We also report some interesting observations on the temporal evolution of the discovered social groups using case studies.

     

基于复杂网络节点重要性的链路预测算法

提升链路预测精度是复杂网络研究的基础问题之一,现有的基于节点相似的链路预测指标没有充分利用网络节点的重要性,即节点在网络中的影响力。针对以上问题提出基于节点重要性的链路预测算法。该算法在基于局部相似性链路预测算法的共同邻居（CN）、Adamic-Adar（AA）、Resource Allocation（RA）相似性指标的基础上,充分利用了节点度中心性、接近中心性及介数中心性的信息,提出考虑节点重要性的CN、AA、RA链路预测相似性指标。在4个真实数据集上进行仿真实验,以AUC值作为链路预测精度评价指标,实验结果表明,改进的算法在4个数据集上的链路预测精度均高于共同邻居等对比算法,能够对复杂网络结构产生更精确的分析预测。