Weighted Complex Networks Research Articles

A novel visibility graph transformation of time series into weighted networks

Analyzing time series from the perspective of complex network has interested many scientists. In this paper, based on visibility graph theory a novel method of constructing weighted complex network from time series is proposed. The first step is to determine the weights of vertices in time series, which linearly combines the weights generated by induced ordered averaging aggregation operator (IOWA) and visibility graph aggregation operator (VGA). Then, two strategies, averaging strategy and gravity strategy, are proposed to construct weighted network. To testify the validity of proposed method, an artificial case is adopted, in which link prediction is used to evaluate the performance of the weighted network. It is shown that the weighted network constructed by proposed method greatly outperforms the unweighted network obtained by traditional visibility graph theory.

Measuring health of highway network configuration against dynamic Origin-Destination demand network using weighted complex network analysis.

Ideal configuration or layout of highways should resemble the actual demands for the roads represented by Origin-Destination (OD) information. It would be beneficial if existing highways can be evaluated for their configurational fitness against the current demands, and newly planned highways can carefully be designed in terms of their layouts and topologies that would reflect the demands. Analysis techniques used for complex networks in the matured field of network theory can be applied for the highway layout health monitoring against the current OD information. This paper proposes a methodology of measuring the fitness of existing highways by comparing their structural configuration against conceptual OD networks using well-established techniques in network theory for complex networks. In the first phase, this paper conducts an empirical analysis and finds that both structural highway network and OD network follow the “power law” distribution as they are weighted by capacity and traffic volume respectively. It is also found that the power law coefficient of the OD network dynamically changes throughout the day and week. In the second phase, a noble methodology of weighting and measuring the health, of structural highway networks against OD networks by means of comparing their power law coefficients is proposed. It is found that the proposed method is effective at detecting deviations from ideal structural configurations associated with actual demands.

Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.

Disruption of Protein Complexes from Weighted Complex Networks

Essential proteins are indispensable units for living organisms. Removing those leads to disruption of protein complexes and causing lethality. Recently, theoretical methods have been presented to detect essential proteins in protein interaction network. In these methods, an essential protein is predicted as a high-degree vertex of protein interaction network. However, interaction data are usually incomplete and an essential protein cannot have high-connection due to data deficiency. Then, it is critical to design informative networks from other biological data sources. In this paper, we defined a minimal set of proteins to disrupt the maximum number of protein complexes. We constructed a weighted graph using a set of given complexes. We proposed a more appropriate method based on betweenness values to diagnose a minimal set of proteins whose removal would generate the disruption of protein complexes. The effectiveness of the proposed method was benchmarked using given dataset of complexes. The results of our method were compared to the results of other methods in terms of the number of disrupted complexes. Also, results indicated significant superiority of the minimal set of proteins in the massive disruption of complexes. Finally, we investigated the performance of our method for yeast and human datasets and analyzed biological properties of the selected proteins. Our algorithm and some example are freely available from http://bs.ipm.ac.ir/softwares/DPC/DPC.zip.

An efficient immunization strategy based on transmission limit in weighted complex networks

The immunization strategy against the epidemic spreading in real world has attracted widespread attention of scientists from many different fields. However, the traditional immune behavior is achieved by deleting the edges in the network, which can lead to variations in the network structure and consequently serious damage to the efficiency of networks. In this paper, we studied a new type of immune strategy applied to weighted networks, which is to maintain the necessary network efficiency by limit the transmission(reduce the weight of edges) to suppress the spread of epidemic. It is similar to the inflammation around the infected parts of our body, which not only prevent epidemic from further spreading but also do no harm to the function of the body. We first set the rate of transmission be proportional to the edge weight according to the S–I epidemic spreading model. Then, we propose the specific dynamic evolution model for infected nodes that boosts efficient epidemic control. Theoretical analysis and simulation results indicate that the immunization strategy can efficaciously prevent the spread of the epidemic, while maintaining the high efficiency of the network.

The robustness of interdependent weighted networks

We analysis the cascading failure of interdependent weighted networks based on percolation theory and local weighted flow redistribution rule. The weight of a node is Biθ, where Bi is the betweenness of the node. We assume that the two networks A and B of size NA andNB are BA networks, and suppose two different one-to-one interdependent network, one is random, the other based on nodes’ betweenness. Assume that a failed node in network A leads to a redistribution of the flow passing through it to its neighboring nodes and the interdependent node in network B also to be disabled, where the two failure factors happen concurrently, or successively. We find that the one-to-one random interdependent weighted complex network reaches the strongest robustness level when the weight parameter θ =0.5, no matter cascading failure caused by two failure factors happen concurrently, or successively. And when the interdependent relationship based on nodes’ betweenness, θ=0.7 to get the strongest robustness level.

Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks.

In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks. Three null models for topology and weight distribution of weighted networks are presented. All the links of the original network can be divided into strong and weak ties. We can use null models to verify the strong effect of weak or strong ties. For two important statistics, we construct two null models to measure their impacts on link prediction. In our experiments, the proposed method is applied to seven empirical networks, which demonstrates that this model is universal and the impact of the topology and weight distribution of these networks in link prediction can be quantified by it. We find that in the USAir, the Celegans, the Gemo, the Lesmis and the CatCortex, the strong ties are easier to predict, but there are a few networks whose weak edges can be predicted more easily, such as the Netscience and the CScientists. It is also found that the weak ties contribute more to link prediction in the USAir, the NetScience and the CScientists, that is, the strong effect of weak ties exists in these networks. The framework we proposed is versatile, which is not only used to link prediction but also applicable to other directions in complex networks.

Analysis of time-varying characteristics of bus weighted complex network in Qingdao based on boarding passenger volume

Mastering the demand characteristics of a city’s bus travel and understanding the demand structure from time and space are of great significance for a city’s public traffic management. From the point of weighted complex network, this paper constructs the adjacency-stop bus complex network of Qingdao city in China using Space L method, and analyzes topological characteristics of the network. For the first time, by means of node weighting, the space–time characteristics of Qingdao bus travel demand are analyzed from the point of view of node strength. Through the analysis of the distribution characteristics of node strength at different periods of working and non-working days, it is found that node strength overall obeys SPL (Shift Power Law) tending to exponential distribution, which shows that the distribution of passenger flow in Qingdao bus travel is uneven, but not extremely uneven like power-law distribution. Comparing the changes of boarding volume at different time in one day both of working day and non-working day, the key bus stops and pivots of public transportation is extracted; and combined with the spatial distribution characteristics, it is found that there is a high correlation between bus travel demand and spatial attribute in Qingdao City, and a low correlation between bus travel demand and time attribute.

An information dimension of weighted complex networks

The fractal and self-similarity are important properties in complex networks. Information dimension is a useful dimension for complex networks to reveal these properties. In this paper, an information dimension is proposed for weighted complex networks. Based on the box-covering algorithm for weighted complex networks (BCANw), the proposed method can deal with the weighted complex networks which appear frequently in the real-world, and it can get the influence of the number of nodes in each box on the information dimension. To show the wide scope of information dimension, some applications are illustrated, indicating that the proposed method is effective and feasible.

CDA: A Clustering Degree Based Influential Spreader Identification Algorithm in Weighted Complex Network

Identifying the most influential spreaders in a weighted complex network is vital for optimizing utilization of the network structure and promoting the information propagation. Most existing algorithms focus on node centrality, which consider more connectivity than clustering. In this paper, a novel algorithm based on clustering degree algorithm (CDA) is proposed to identify the most influential spreaders in a weighted network. First, the weighted degree of a node is defined according to the node degree and strength. Then, based on the node weighted degree, the clustering degree of a node is calculated in respect to the network topological structure. Finally, the propagation capability of a node is achieved by accounting the clustering degree of the node and the contribution from its neighbors. In order to evaluate the performance of the proposed CDA algorithm, the susceptible-infected-recovered model is adopted to simulate the propagation process in real-world networks. The experiment results have showed that CDA is the most effective algorithm in terms of Kendall’s tau coefficient and with the highest accuracy in influential spreader identification compared with other algorithms such as weighted degree centrality, weighted closeness centrality, evidential centrality, and evidential semilocal centrality.

Coevolution of cooperation and network structure in social dilemmas in evolutionary dynamic complex network

Emergence of cooperation in social dilemmas is an essential phenomena for the functioning of numerous multilevel and complex systems. The evidence of cooperation ranges from the elementary biological organisms to the most sophisticated human societies. Although emergence of cooperation is widely experienced, but its evolution is not well explained, since natural selection typically promotes selfish behaviours which are often not socially optimal. In this paper the coevolution of network structure and emergence of cooperation is studied in four classes of social dilemmas, representing the prisoner's dilemma, Hawk–Dove, snowdrift and coordination classes of games, in structured populations defined by weighted complex networks. The strength of interaction between two individuals is represented by network (edge) weight, which changes according to individuals’ preference through the evolutionary network dynamics. Using evolutionary dynamic network based simulations of the games model on randomly weighted complete networks, we present a detailed study of the evolution of dynamic complex network through the evolution of the structural properties of a network, such as clustering coefficient, assortativity coefficient, entropy of degree distribution, average strength of interaction and the promotion of cooperative behaviour in all four classes of games. The effect of changing the cost-to-benefit ratio on these network properties and evolution of cooperation is also reported.

Module partition of complex mechanical products based on weighted complex networks

It is tough to build an effective mathematical model to describe the complicated relationships in complex mechanical products, which leads to the module partition of complex mechanical products and the guarantee of accurate results become more difficult. In addition, the module partition method cannot bring about a satisfactory module partition result if the scale of the products is huge and complicated. In this case, complex network theory is used to solve these problems in this paper. Firstly, a weighted complex network is established to systematically express the structure of complex mechanical products. In particular, customer demands are taken into account for module partition by introducing customer involvement. Secondly, the interval-valued intuitionistic fuzzy sets are used to calculate the relationships between parts for reducing the subjectivity of the calculation process. Afterwards, a modified GN algorithm (community detection algorithm) is proposed to achieve the module partition of complex mechanical products. Finally, the module partition of a wind turbine is carried out to verify the effectiveness of the proposed method in this paper. The result of the case study shows that the modified GN algorithm achieves better module partition performance than the classical GN algorithm and fuzzy clustering analysis method, which obtains a satisfactory result for applications.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

AbstractCurrent researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.

Automatic clustering constraints derivation from object-oriented software using weighted complex network with graph theory analysis

Abstract Constrained clustering or semi-supervised clustering has received a lot of attention due to its flexibility of incorporating minimal supervision of domain experts or side information to help improve clustering results of classic unsupervised clustering techniques. In the domain of software remodularisation, classic unsupervised software clustering techniques have proven to be useful to aid in recovering a high-level abstraction of the software design of poorly documented or designed software systems. However, there is a lack of work that integrates constrained clustering for the same purpose to help improve the modularity of software systems. Nevertheless, due to time and budget constraints, it is laborious and unrealistic for domain experts who have prior knowledge about the software to review each and every software artifact and provide supervision on an on-demand basis. We aim to fill this research gap by proposing an automated approach to derive clustering constraints from the implicit structure of software system based on graph theory analysis of the analysed software. Evaluations conducted on 40 open-source object-oriented software systems show that the proposed approach can serve as an alternative solution to derive clustering constraints in situations where domain experts are non-existent, thus helping to improve the overall accuracy of clustering results.

Classify epileptic EEG signals using weighted complex networks based community structure detection

Abstract Background Epilepsy is a brain disorder that is mainly diagnosed by neurologists based on electroencephalogram (EEG) recordings. Epileptic EEG signals are recorded as multichannel signals. A reliable technique for analysing multi-channel EEG signals is in urgent demand for the treatment and diagnosis of patients who have epilepsy and other brain disorders. Method In this paper, each single EEG channel is partitioned into four segments, with each segment is further divided into small clusters. A set of statistical features are extracted from each cluster. As a result, a vector of all the features from each EEG single channel is obtained. The resulting features vector is then mapped into an undirected weighted network. The modularity of the networks is found to be the best to detect epileptic seizures in EEG signals. Other local and global network features, including clustering coefficients, average degree and closeness centrality, are also extracted and studied. All the network attributes are ranked based on their potential to detect abnormalities in EEG signals. Results Eight pairs of combinations of EEG signals are classified by the proposed method using four well known classifiers: a least support vector machine, k -means, Naive Bayes, and K -nearest. The proposed method achieved an average of 98%, 96.5%, 99%, rand 0.012, respectively, for its accuracy, sensitivity, specificity and the false positive rate. Comparisons were made using several existing epileptic seizures detection methods using the same datasets. The obtained results showed that the proposed method was efficient in detecting epileptic seizures in EEG signals.

Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications

Through an elegant geometrical interpretation, the multi-fractal analysis quantifies the spatial and temporal irregularities of the structural and dynamical formation of complex networks. Despite its effectiveness in unweighted networks, the multi-fractal geometry of weighted complex networks, the role of interaction intensity, the influence of the embedding metric spaces and the design of reliable estimation algorithms remain open challenges. To address these challenges, we present a set of reliable multi-fractal estimation algorithms for quantifying the structural complexity and heterogeneity of weighted complex networks. Our methodology uncovers that (i) the weights of complex networks and their underlying metric spaces play a key role in dictating the existence of multi-fractal scaling and (ii) the multi-fractal scaling can be localized in both space and scales. In addition, this multi-fractal characterization framework enables the construction of a scaling-based similarity metric and the identification of community structure of human brain connectome. The detected communities are accurately aligned with the biological brain connectivity patterns. This characterization framework has no constraint on the target network and can thus be leveraged as a basis for both structural and dynamic analysis of networks in a wide spectrum of applications.

Information mining in weighted complex networks with nonlinear rating projection

Weighted rating networks are commonly used by e-commerce providers nowadays. In order to generate an objective ranking of online items’ quality according to users’ ratings, many sophisticated algorithms have been proposed in the complex networks domain. In this paper, instead of proposing new algorithms we focus on a more fundamental problem: the nonlinear rating projection. The basic idea is that even though the rating values given by users are linearly separated, the real preference of users to items between the different given values is nonlinear. We thus design an approach to project the original ratings of users to more representative values. This approach can be regarded as a data pretreatment method. Simulation in both artificial and real networks shows that the performance of the ranking algorithms can be improved when the projected ratings are used.

Weighted complex network analysis of the Beijing subway system: Train and passenger flows

In recent years, complex network theory has become an important approach to the study of the structure and dynamics of traffic networks. However, because traffic data is difficult to collect, previous studies have usually focused on the physical topology of subway systems, whereas few studies have considered the characteristics of traffic flows through the network. Therefore, in this paper, we present a multi-layer model to analyze traffic flow patterns in subway networks, based on trip data and an operation timetable obtained from the Beijing Subway System. We characterize the patterns in terms of the spatiotemporal flow size distributions of both the train flow network and the passenger flow network. In addition, we describe the essential interactions between these two networks based on statistical analyses. The results of this study suggest that layered models of transportation systems can elucidate fundamental differences between the coexisting traffic flows and can also clarify the mechanism that causes these differences.

Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

Mining Important Nodes in Directed Weighted Complex Networks

In complex networks, mining important nodes has been a matter of concern by scholars. In recent years, scholars have focused on mining important nodes in undirected unweighted complex networks. But most of the methods are not applicable to directed weighted complex networks. Therefore, this paper proposes a Two-Way-PageRank method based on PageRank for further discussion of mining important nodes in directed weighted complex networks. We have mainly considered the frequency of contact between nodes and the length of time of contact between nodes. We have considered the source of the nodes (in-degree) and the whereabouts of the nodes (out-degree) simultaneously. We have given node important performance indicators. Through numerical examples, we analyze the impact of variation of some parameters on node important performance indicators. Finally, the paper has verified the accuracy and validity of the method through empirical network data.