Identifying influential nodes in complex networks

Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible-Infected-Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.     

Nodes and layers PageRank centrality for multilayer networks

In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks(i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.     

基于层间相似性的时序网络节点重要性研究

时序网络可以更加准确地描述节点之间的交互顺序和交互关系.结合多层耦合网络分析法,本文提出了基于节点层间相似性的超邻接矩阵时序网络节点重要性识别方法,与经典的认为所有层间关系为常数不同,层间关系用节点的邻居拓扑重叠系数进行度量.Workspace和Enrons数据集上的结果显示:相比经典的方法,使用该方法得到的Kendall’sτ值在各时间层上的平均提高,最高为17.72%和12.44%,结果表明层间相似性的度量对于时序网络的节点重要性度量具有十分重要的意义.     

A modified evidential methodology of identifying influential nodes in weighted networks

How to identify influential nodes in complex networks is still an open hot issue. In the existing evidential centrality (EVC), node degree distribution in complex networks is not taken into consideration. In addition, the global structure information has also been neglected. In this paper, a new Evidential Semi-local Centrality (ESC) is proposed by modifying EVC in two aspects. Firstly, the Basic Probability Assignment (BPA) of degree generated by EVC is modified according to the actual degree distribution, rather than just following uniform distribution. BPA is the generation of probability in order to model uncertainty. Secondly, semi-local centrality combined with modified EVC is extended to be applied in weighted networks. Numerical examples are used to illustrate the efficiency of the proposed method.     

Epidemic centrality — is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as “superspreaders”, are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed.     

LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks

Identifying influential nodes in complex networks is one of the most significant and challenging issues, which may contribute to optimizing the network structure, controlling the process of epidemic spreading and accelerating information diffusion. The node importance ranking measures based on global information are not suitable for large-scale networks due to their high computational complexity. Moreover, they do not take into account the impact of network topology evolution over time, resulting in limitations in some applications. Based on local information of networks, a local clustering H-index (LCH) centrality measure is proposed, which considers neighborhood topology, the quantity and quality of neighbor nodes simultaneously. The proposed measure only needs the information of first-order and second-order neighbor nodes of networks, thus it has nearly linear time complexity and can be applicable to large-scale networks. In order to test the proposed measure, we adopt the susceptible-infected-recovered (SIR) and susceptible-infected (SI) models to simulate the spreading process. A series of experimental results on eight real-world networks illustrate that the proposed LCH can identify and rank influential nodes more accurately than several classical and state-of-the-art measures.     

一种复杂网络路由策略的普适优化算法

现有的复杂网络路由策略很多,改进算法也不断涌现,但是目前还没有一个统一的标准来衡量算法是否达到网络最佳传输效果.针对这一问题,本文提出一种适用于现有路由策略的普适优化算法.首先通过理论分析指出制约网络传输能力的关键因素是最大介数中心度,因而"最大介数中心度是否已经最低"成为评判路由策略是否最优的标准.在此基础上,采用"惩罚选择法"避开网络中介数中心度值比较大的节点,使网络介数中心度值分布更均匀,均衡网络中各个节点的传输负载.仿真结果显示,该优化算法针对现有路由策略均能降低最大介数中心度值,大幅度提高网络的传输能力.     

Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities

Despite recent advances in the study of temporal networks, the analysis of time-stampednetwork data is still a fundamental challenge. In particular, recent studies have shownthat correlations in the ordering of links crucially alter causaltopologies of temporal networks, thus invalidating analyses based on static,time-aggregated representations of time-stamped data. These findings not only highlight animportant dimension of complexity in temporal networks, but also call for newnetwork-analytic methods suitable to analyze complex systems with time-varying topologies.Addressing this open challenge, here we introduce a novel framework for the study ofpath-based centralities in temporal networks. Studying betweenness,closeness and reach centrality, we first show than an application of these measures totime-aggregated, static representations of temporal networks yields misleading resultsabout the actual importance of nodes. To overcome this problem, we define path-basedcentralities in higher-order aggregate networks, a recently proposedgeneralization of the commonly used static representation of time-stamped data. Using dataon six empirical temporal networks, we show that the resulting higher-order measuresbetter capture the true, temporal centralities of nodes. Our resultsdemonstrate that higher-order aggregate networks constitute a powerful abstraction, withbroad perspectives for the design of new, computationally efficient data mining techniquesfor time-stamped relational data.     

Identifying influential nodes in weighted networks based on evidence theory

The design of an effective ranking method to identify influential nodes is an important problem in the study of complex networks. In this paper, a new centrality measure is proposed based on the Dempster–Shafer evidence theory. The proposed measure trades off between the degree and strength of every node in a weighted network. The influences of both the degree and the strength of each node are represented by basic probability assignment (BPA). The proposed centrality measure is determined by the combination of these BPAs. Numerical examples are used to illustrate the effectiveness of the proposed method.     

利用邻域“结构洞”寻找社会网络中最具影响力节点

识别复杂网络中的关键节点对网络结构优化和鲁棒性增强具有十分重要的意义. 经典的关键节点测量方法在一定程度上能够辨识网络中影响力节点, 但存在一定局限性: 局部中心性测量方法仅考虑节点邻居的数目, 忽略了邻居间的拓扑关系, 不能在计算中反映邻居节点间的相互作用; 全局测量方法则由于算法本身的复杂性而不能应用于大规模社会网络的分析, 另外, 经典的关键节点测量方法也没有考虑社会网络特有的社区特征. 为高效、准确地辨识具有社区结构的社会网络中最具影响力节点, 提出了一种基于节点及其邻域结构洞的局部中心性测量方法, 该方法综合考虑了节点的邻居数量及其与邻居间的拓扑结构, 在节点约束系数的计算中同时体现了节点的度属性和“桥接”属性. 利用SIR(易感-感染-免疫)模型在真实社会网络数据上对节点传播能力进行评价后发现, 所提方法可以准确地评价节点的传播能力且具有强的鲁棒性.     

Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies

We present a model of complex network generated from Hang Seng index (HSI) of Hong Kong stock market, which encodes stock market relevant both interconnections and interactions between fluctuation patterns of HSI in the network topologies. In the network, the nodes (edges) represent all kinds of patterns of HSI fluctuation (their interconnections). Based on network topological statistic, we present efficient algorithms, measuring betweenness centrality (BC) and inverse participation ratio (IPR) of network adjacency matrix, for detecting topological important nodes. We have at least obtained three uniform nodes of topological importance, and find the three nodes, i.e. 18.7% nodes undertake 71.9% betweenness centrality and closely correlate other nodes. From these topological important nodes, we can extract hidden significant fluctuation patterns of HSI. We also find these patterns are independent the time intervals scales. The results contain important physical implication, i.e. the significant patterns play much more important roles in both information control and transport of stock market, and should be useful for us to more understand fluctuations regularity of stock market index. Moreover, we could conclude that Hong Kong stock market, rather than a random system, is statistically stable, by comparison to random networks.     

A Path-Based Distribution Measure for Network Comparison

As network data increases, it is more common than ever for researchers to analyze a set of networks rather than a single network and measure the difference between networks by developing a number of network comparison methods. Network comparison is able to quantify dissimilarity between networks by comparing the structural topological difference of networks. Here, we propose a kind of measures for network comparison based on the shortest path distribution combined with node centrality, capturing the global topological difference with local features. Based on the characterized path distributions, we define and compare network distance between networks to measure how dissimilar the two networks are, and the network entropy to characterize a typical network system. We find that the network distance is able to discriminate networks generated by different models. Combining more information on end nodes along a path can further amplify the dissimilarity of networks. The network entropy is able to detect tipping points in the evolution of synthetic networks. Extensive numerical simulations reveal the effectivity of the proposed measure in network reduction of multilayer networks, and identification of typical system states in temporal networks as well.     

交织型层级复杂网

为研究两个异质关联网络复合后的结构特征与节点中心性特征,本文提出了交织型层级复杂网络的概念,可描述由两个具有部分相同节点,连接边属性近似的子网所构成的层级复杂网络,并定义了节点交织系数、路径交织系数和网络交织系数3种测度用于衡量两个子网之间的密切程度.针对该类网络,研究并改进了节点度中心性和介数中心性的计算方法,同时提出一种新的中心性指标—助联性,用于衡量子网的某一节点对另一子网联通性和流通性的助益.通过实验分析,验证了本文各类指标的有效性.     

Enhancing robustness and synchronizability of networks homogenizing their degree distribution

A new family of networks, called entangled, has recently been proposed in the literature. These networks have optimal properties in terms of synchronization, robustness against errors and attacks, and efficient communication. They are built with an algorithm which uses modified simulated annealing to enhance a well-known measure of networks’ ability to reach synchronization among nodes. In this work, we suggest that a class of networks similar to entangled networks can be produced by changing some of the connections in a given network, or by just adding a few connections. We call this class of networks weak-entangled. Although entangled networks can be considered as a subset of weak-entangled networks, we show that both classes share similar properties, especially with respect to synchronization and robustness, and that they have similar structural properties.     

Lobby index in networks

We propose a new node centrality measure in networks, the lobby index, which is inspired by Hirsch’s h-index. It is shown that in scale-free networks with exponent α the distribution of the l-index has power tail with exponent α(α+1). Properties of the l-index and extensions are discussed.     

Target recovery in complex networks

The invulnerability of complex networks is an important issue which has been widely analyzed in different fields. A lot of works have been done to measure and improve the stability of complex networks when being attacked. Recently, how to recover networks after attack was intensively studied. The existing methods are mainly designed to recover the overall functionality of networks, yet in many real cases the recovery of important nodes should be given priority, to which we refer target recovery. For example, when the cold wave paralyses the railway networks, target recovery means to repair those stations or railways such that the transport capacity of densely-populated cities can be recovered as fast as possible. In this paper, we first compare the impact of attacks on the whole network and target nodes respectively, and then study the efficiency of traditional recovery methods that are proposed based on global centrality metrics. Furthermore, based on target centrality metrics, we introduce a local betweenness recovery method and we find it has better performance than the traditional methods. We finally propose a hybrid recovery method which includes local betweenness metric and local closeness metric. The performance of the hybrid method is shown to be similar to that of the greedy algorithm.     

The emergence of scale-free networks with a seceding mechanism

In order to explore further the underlying mechanism of scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new nodes, the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we obtain an analytical expression of the power-law degree distribution with scaling exponent γ ranging from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results.     

Identifying important nodes in weighted functional brain networks: a comparison of different centrality approaches

We compare different centrality metrics which aim at an identification of important nodes in complex networks. We investigate weighted functional brain networks derived from multichannel electroencephalograms recorded from 23 healthy subject under resting-state eyes-open or eyes-closed conditions. Although we observe the metrics strength, closeness, and betweenness centrality to be related to each other, they capture different spatial and temporal aspects of important nodes in these networks associated with behavioral changes. Identifying and characterizing of these nodes thus benefits from the application of several centrality metrics.     

基于区域密度曲线识别网络上的多影响力节点

复杂网络多影响力节点的识别可以帮助理解网络的结构和功能,具有重要的理论意义和应用价值.本文提出一种基于网络区域密度曲线的多影响力节点的识别方法.应用两种不同的传播模型,在不同网络上与其他中心性指标进行了比较.结果表明,基于区域密度曲线的识别方法能够更好地识别网络中的多影响力节点,选中的影响力节点之间的分布较为分散,自身也比较重要.本文所提方法是基于网络的局部信息,计算的时间复杂度较低.     

Lobby index as a network centrality measure

We study the lobby index (l$l$-index for short) as a local node centrality measure for complex networks. The l$l$-index is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of a biological network (Yeast interaction protein–protein network) and a linguistic network (Moby Thesaurus   II). In both networks, the l$l$-index has a poor correlation with betweenness but correlates with degree and Eigenvector centralities. Although being local, the l$l$-index carries more information about its neighbors than degree centrality. Also, it requires much less time to compute when compared with Eigenvector centrality. Results show that the l$l$-index produces better results than degree and Eigenvector centrality for ranking purposes.