Ranking the spreading influence in complex networks

Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node and the node set with the highest k$k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barabási–Albert network, the parameterless method could identify the node spreading influence more accurately than the ones generated by the degree k$k$, closeness centrality, k$k$-shell and mixed degree decomposition methods. This work would be helpful for deeply understanding the node importance of a network.     

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.     

Hybrid phase transitions of spreading dynamics in multiplex networks

In this paper, we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals depending on whether they realize the spreading or not. We model the system with a two-layer multiplex network, in which one layer describes the spreading of social behaviors and the other layer describes the diffusion of the awareness about the spreading. We use the susceptible-infected-susceptible (SIS) model to describe the dynamics of an individual if it is unaware of the spreading of the behavior. While when an individual is aware of the spreading of the social behavior its dynamics will follow the threshold model, in which an individual will adopt a behavior only when the fraction of its neighbors who have adopted the behavior is above a certain threshold. We find that such heterogenous reactions can induce intriguing dynamical properties. The dynamics of the whole network may exhibit hybrid phase transitions with the coexistence of continuous phase transition and bi-stable states. Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided. The results are supported by theoretical analysis.     

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.     

Self-similar scaling of density in complex real-world networks

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome of the evolution of real-world systems has also attracted much attention within the physics literature. Here we investigate the scaling of density in complex networks under two classical box-covering renormalizations–network coarse-graining–and also different community-based renormalizations. The analysis on over 50 real-world networks reveals a power-law scaling of network density and size under adequate renormalization technique, yet irrespective of network type and origin. The results thus advance a recent discovery of a universal scaling of density among different real-world networks [P.J. Laurienti, K.E. Joyce, Q.K. Telesford, J.H. Burdette, S. Hayasaka, Universal fractal scaling of self-organized networks, Physica A 390 (20) (2011) 3608–3613] and imply an existence of a scale-free density also within–among different self-similar scales of–complex real-world networks. The latter further improves the comprehension of self-similar structure in large real-world networks with several possible applications.     

Reducing congestion on complex networks by dynamic relaxation processes

We study the effects of relaxational dynamics on the congestion pressure in general transport networks. We show that the congestion pressure is reduced in scale-free networks if a relaxation mechanism is utilized, while this is in general not the case for non-scale-free graphs such as random graphs. We also present evidence supporting the idea that the emergence of scale-free networks arise from optimization mechanisms to balance the load of the networks nodes.     

Approaching human language with complex networks

The interest in modeling and analyzing human language with complex networks is on the rise in recent years and a considerable body of research in this area has already been accumulated. We survey three major lines of linguistic research from the complex network approach: 1) characterization of human language as a multi-level system with complex network analysis; 2) linguistic typological research with the application of linguistic networks and their quantitative measures; and 3) relationships between the system-level complexity of human language (determined by the topology of linguistic networks) and microscopic linguistic (e.g., syntactic) features (as the traditional concern of linguistics). We show that the models and quantitative tools of complex networks, when exploited properly, can constitute an operational methodology for linguistic inquiry, which contributes to the understanding of human language and the development of linguistics. We conclude our review with suggestions for future linguistic research from the complex network approach: 1) relationships between the system-level complexity of human language and microscopic linguistic features; 2) expansion of research scope from the global properties to other levels of granularity of linguistic networks; and 3) combination of linguistic network analysis with other quantitative studies of language (such as quantitative linguistics).     

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     

Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence(IS) to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.     

Detecting the structure of complex networks by quantum bosonic dynamics

In this paper, we introduce a non-interacting boson model to investigate the topological structure of complex networks. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of realistic networks. We find that the ground-state degeneracy of this model is equal to the number of connected components in a network and the square of each coefficient in the expansion of the ground state gives the average time that a random walker spends at each node in the infinite time limit. To show the usefulness of this approach in practice, we also carry out numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods. Furthermore, we show that the first excited state appears always on the largest connected component of the network. The relationship between the first excited energy and the average shortest path length in networks is also discussed.     

基于扩展度的复杂网络传播影响力评估算法

对网络中节点的传播影响力进行评估具有十分重要的意义, 有助于促进有益或抑制有害信息的传播. 目前, 多种中心性指标可用于对节点的传播影响力进行评估, 然而它们一般只有当传播率处于特定范围时才能取得理想的结果. 例如, 度值中心性指标在传播率较小时较为合适, 而半局部中心性和接近中心性指标则适用于稍大一些的传播率. 为了解决各种评估指标对传播率敏感的问题, 提出了一种基于扩展度的传播影响力评估算法. 算法利用邻居节点度值叠加的方式对节点度的覆盖范围进行了扩展, 使不同的扩展层次对应于不同的传播率, 并通过抽样测试确定了适合于特定传播率的层次数. 真实和模拟数据集上的实验结果表明, 通过扩展度算法得到的扩展度指标能在不同传播率下对节点的传播影响力进行有效评估, 其准确性能够达到或优于利用其他中心性指标进行评估的结果.     

Motif structure and cooperation in real-world complex networks

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.     

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of São Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model.     

A review of fractality and self-similarity in complex networks

We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a self-similar picture under renormalization of the length scale. These results have an important effect in our understanding of the evolution and behavior of such systems. A large number of network properties can now be described through a set of simple scaling exponents, in analogy with traditional fractal theory.     

Spectral reconstruction of complex networks

In this paper we study the reconstruction of a network topology from the eigenvalues of its Laplacian matrix. We introduce a simple cost function and consider the tabu search combinatorial optimization method, while comparing its performance when reconstructing different categories of networks-random, regular, small-world, scale-free and clustered-from their eigenvalues. We show that this combinatorial optimization method, together with the information contained in the Laplacian spectrum, allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders. We also show that the method can be used to generate a quasi-optimal topology for a network associated to a dynamic process (like in the case of metabolic or protein-protein interaction networks of organisms).     

Threshold model of cascades in empirical temporal networks

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. In many cases, bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work we propose an extension of Watts’s classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds in the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model’s behavior, we run the model on real and randomized empirical contact datasets.     

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.     

Detecting communities by the core-vertex and intimate degree in complex networks

In this paper, we present a new approach to extract communities in the complex networks with considerable accuracy. We introduce the core-vertex and the intimate degree between the community and its neighboring vertices. First, we find the core-vertices as the initial community. These core-vertices are then expanded using intimate degree function during extracting community structure from the given network. In addition, our algorithm successfully finds common nodes between communities. Experimental results using some real-world networks data shows that the performance of our algorithm is satisfactory.     

Mixing search on complex networks

In this article, we derive the first passage time (FPT) distribution and the mean first passage time (MFPT) of random walks from multiple sources on networks. On the basis of analysis and simulation, we find that the MFPT drops substantially when particle number increases at the first stage, and converges to the shortest distance between the sources and the destination when particle number tends to infinite. Given the fact that a Brownian particle from a high-degree node often needs a large number of steps to reach an expected low-degree node, which is the bottleneck for a single random walk, we propose a mixing search model to improve the efficiency of search processes by using random walks from multiple sources to continue the searches from high-degree nodes to destinations. We compare our model with the mixing navigation model proposed by Zhou on complex networks and find that our model converges much faster with lower hardware cost than Zhou’s model. Moreover, simulations on scale-free networks show that the search efficiency of our model is much higher than that of a single random walk, and comparable to that of multiple random walks which have much higher hardware cost than our model. Finally, we discuss the traffic cost of our model, and propose an absorption strategy for our model to recover the additional walkers in networks. Simulations indicate that this strategy reduces the traffic cost of our model effectively.