节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.     

一种新的网络传播中最有影响力的节点发现方法

在复杂网络的传播模型研究中, 如何发现最具影响力的传播节点在理论和现实应用中都有重大的意义. 目前的研究一般使用节点的度数、紧密度、介数和K-shell等中心化指标来评价影响力, 这种方法虽然简单, 但是由于它们仅利用了节点自身的内部属性, 因而在评价影响力时精确度并不高, 普遍性适用性较弱.为了解决这个问题, 本文提出了KSC (K-shell and community centrality)指标模型. 此模型不但考虑了节点的内部属性, 而且还综合考虑了节点的外部属性, 例如节点所属的社区等. 然后利用SIR (susceptible-infected-recovered)模型对传播过程进行仿真, 实验证明所提出的方法可以更好地发现最具有影响力的节点, 且可适用于各种复杂网络. 本文为这项具有挑战性研究提供了新的思想和方法. 关键词： 复杂网络 最具影响力的节点 社区划分 中性化测量     

A framework to approach problems of forensic anthropology using complex networks

We have developed a method to analyze and interpret emerging structures in a set of data which lacks some information. It has been conceived to be applied to the problem of getting information about people who disappeared in the Argentine state of Tucumán from 1974 to 1981. Even if the military dictatorship formally started in Argentina had begun in 1976 and lasted until 1983, the disappearance and assassination of people began some months earlier. During this period several circuits of Illegal Detention Centres (IDC) were set up in different locations all over the country. In these secret centres, disappeared people were illegally kept without any sort of constitutional guarantees, and later assassinated. Even today, the final destination of most of the disappeared people’s remains is still unknown. The fundamental hypothesis in this work is that a group of people with the same political affiliation whose disappearances were closely related in time and space shared the same place of captivity (the same IDC or circuit of IDCs). This hypothesis makes sense when applied to the systematic method of repression and disappearances which was actually launched in Tucumán, Argentina (2007) [11]. In this work, the missing individuals are identified as nodes on a network and connections are established among them based on the individuals’ attributes while they were alive, by using rules to link them. In order to determine which rules are the most effective in defining the network, we use other kind of knowledge available in this problem: previous results from the anthropological point of view (based on other sources of information, both oral and written, historical and anthropological data, etc.); and information about the place (one or more IDCs) where some people were kept during their captivity. For these best rules, a prediction about these people’s possible destination is assigned (one or more IDCs where they could have been kept), and the success of the prediction is evaluated. By applying this methodology, we have been successful in 71% of the cases. The best rules take into account the proximity of the locations where the kidnappings took place, and link events which occurred in periods of time from 5 to 7 days. Finally, we used one of the best rules to build a network of IDCs in an attempt to formalize the relation between the illegal detention centres. We found that this network makes sense because there are survivors’ testimonies which confirm some of these connections.     

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks, solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.     

Routing in scale-free networks based on expanding betweenness centrality

In this paper, an improved routing strategy is proposed for enhancing the traffic capacity of scale-free networks. Instead of using the information of degree and betweenness centrality, the new algorithm is derived on the basis of the expanding betweenness centrality of nodes, which gives an estimate of the traffic handled by the vertex for a certain route set. Since the nodes with large betweenness centrality are more susceptible to traffic congestion, the traffic can be improved by redistributing traffic loads from nodes with large betweenness centrality to nodes with small betweenness centrality in the process of computing the collective routing table. Comparing with results of previous routing strategies, it is shown that the present improved routing performs more effectively.     

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.     

Attack structural vulnerability of power grids: A hybrid approach based on complex networks

Power grids have been studied as a typical example of real-world complex networks. Different from previous methods, this paper proposes a hybrid approach for structural vulnerability analysis of power transmission networks, in which a DC power flow model with hidden failures is embedded into the traditional error and attack tolerance methodology to form a new scheme for power grids vulnerability assessment and modeling. The new approach embodies some important characteristics of power transmission networks. Furthermore, the simulation on the standard IEEE 118 bus system demonstrates that a critical region might exist and when the power grid operates in the region, it is vulnerable to both random and intentional attacks. Finally, a brief theoretical analysis is presented to explain the new phenomena.     

Analysis and models of bilateral investment treaties using a social networks approach

Bilateral investment treaties (BITs) are agreements between two countries for the reciprocal encouragement, promotion and protection of investments in each other’s territories by companies based in either country. Germany and Pakistan signed the first BIT in 1959 and since then, BITs are one of the most popular and widespread form of international agreement. In this work we study the proliferation of BITs using a social networks approach. We propose a network growth model that dynamically replicates the empirical topological characteristics of the BIT network.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

A generalized approach to complex networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.     

A Monte Carlo model for networks between professionals and society

We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, P(k)∼k^-γ$P(k)\sim k^{-\gamma }$, with γ$\gamma$ ranging from 0.2$0.2$ to 0.5$0.5$, small-world properties, with a network diameter following D(N)∼logN$D(N)\sim \log N$ and relative high clustering, following C(N)∼1/N$C(N)\sim 1/N$ and C(k)∼k^-α$C(k)\sim k^{-\alpha }$, with α$\alpha$ close to 3. We compare our results with data from real-world protein interaction networks.     

Optimal navigation for characterizing the role of the nodes in complex networks

In this paper, we explore how the approach of optimal navigation (Cajueiro (2009) [33]) can be used to evaluate the centrality of a node and to characterize its role in a network. Using the subway network of Boston and the London rapid transit rail as proxies for complex networks, we show that the centrality measures inherited from the approach of optimal navigation may be considered if one desires to evaluate the centrality of the nodes using other pieces of information beyond the geometric properties of the network. Furthermore, evaluating the correlations between these inherited measures and classical measures of centralities such as the degree of a node and the characteristic path length of a node, we have found two classes of results. While for the London rapid transit rail, these inherited measures can be easily explained by these classical measures of centrality, for the Boston underground transportation system we have found nontrivial results.     

Kinetics of node splitting in evolving complex networks

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k$k$ into k$k$ nodes of degree 1$1$. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p$p$, or splitting with probability 1−p$1-p$. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.     

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate.     

Detecting community structure in complex networks via node similarity

The detection of the community structure in networks is beneficial to understand the network structure and to analyze the network properties. Based on node similarity, a fast and efficient method for detecting community structure is proposed, which discovers the community structure by iteratively incorporating the community containing a node with the communities that contain the nodes with maximum similarity to this node to form a new community. The presented method has low computational complexity because of requiring only the local information of the network, and it does not need any prior knowledge about the communities and its detection results are robust on the selection of the initial node. Some real-world and computer-generated networks are used to evaluate the performance of the presented method. The simulation results demonstrate that this method is efficient to detect community structure in complex networks, and the ZLZ metrics used in the proposed method is the most suitable one among local indices in community detection.     

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.     

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.     

Ranking the spreading influence of nodes in complex networks: An extended weighted degree centrality based on a remaining minimum degree decomposition

Ranking the spreading influence of nodes is crucial for developing strategies to control the spreading process on complex networks. In this letter, we define, for the first time, a remaining minimum degree (RMD) decomposition by removing the node(s) with the minimum degree iteratively. Based on the RMD decomposition, a weighted degree (WD) is presented by utilizing the RMD indices of the nearest neighbors of a node. WD assigns a weight to each degree of this node, which can distinguish the contribution of each degree to the spreading influence. Further, an extended weighted degree (EWD) centrality is proposed by extending the WD of the nearest neighbors of a node. Assuming that the spreading process on networks follows the Susceptible-Infectious-Recovered (SIR) model, we perform extensive experiments on a series of synthetic and real networks to comprehensively evaluate the performance of EWD and other eleven representative measures. The experimental results show that EWD is a relatively efficient measure in running efficiency, it exposes an advantage in accuracy in the networks with a relatively small degree heterogeneity, as well as exposes a competitive performance in resolution.