Weighted Complex Networks Research Articles

Vulnerability assessment and reconfiguration of microgrid through search vector artificial physics optimization algorithm

Taking the mathematical model and reliability parameters of the microgrid into account, this paper has proposed two vulnerability assessment indices (VAI) – weighted complex network structure parameters and comprehensive operational sensitivity to set up a vulnerability assessment system. The microgrid reconfiguration (MR) model is built with consideration of the grid-connected/island mode and the VAI. A novel artificial physics optimization algorithm with a searching vector (SVAPO) is presented and applied to minimize the system vulnerability. The technique has been successfully implemented on CERTS and 38-bus microgrids to demonstrate the performance and effectiveness of the proposed method. The results obtained are encouraging.

An integrated module partition approach for complex products and systems based on weighted complex networks

The modularisation strategy can dramatically shorten the lead time and reduce the cost of complex products and systems (CoPS) development. Module partition is the basis of the modularisation. Because of the high technical content and multi-dimensional complexity of CoPS, the existing module partition approach cannot identify the module of CoPS effectively and efficiently. The complex network is introduced to visually represent the CoPS as their topological structures are very similar. The weights of the edges in the weighted complex network (WCN) are brought to illustrate the correlation strengths among components. An integrated approach is proposed in this article by modelling the CoPS module partition problem as the community detection problem of WCN. Firstly, the CoPS component-WCN is constructed and transformed to a multi-graph. Secondly, the modified GN algorithm is adopted to establish the community detection, namely module partition of CoPS. Finally, a module partition case example of a large tonnage crawler crane expounds that the proposed approach is effective and systematic to solve the CoPS module partition problem.

Epidemic spreading on weighted complex networks

Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results once the average weight of whole network is fixed. This work may shed some light on the in-depth understanding of epidemic spreading on multi-relation and weighted networks.

An Adaptive Particle Swarm Optimization Algorithm Based on Directed Weighted Complex Network

The disadvantages of particle swarm optimization (PSO) algorithm are that it is easy to fall into local optimum in high-dimensional space and has a low convergence rate in the iterative process. To deal with these problems, an adaptive particle swarm optimization algorithm based on directed weighted complex network (DWCNPSO) is proposed. Particles can be scattered uniformly over the search space by using the topology of small-world network to initialize the particles position. At the same time, an evolutionary mechanism of the directed dynamic network is employed to make the particles evolve into the scale-free network when the in-degree obeys power-law distribution. In the proposed method, not only the diversity of the algorithm was improved, but also particles’ falling into local optimum was avoided. The simulation results indicate that the proposed algorithm can effectively avoid the premature convergence problem. Compared with other algorithms, the convergence rate is faster.

Explosive transitions to synchronization in weighted static scale-free networks

The emergence of explosive synchronization transitions in networks of phase oscillators has become recently one of the most interesting topics. We simulate the Kuramoto model on top of a family of weighted static scale-free networks. It is found that when the strength of the network’s edge is linearly correlated with frequency gap of pair of oscillators at its ends, i.e., the microscopic correlation exponent β is equal to 1, the model with the degree distribution exponent γ > 3 undergoes a first-order phase transition, while the transition becomes second order at 2 < γ ≤ 3. We also find that in homogeneous networks (γ → ∞) the explosive synchronization is replaced by a continuous phase transition when the microscopic correlation exponent β is changed from positive to negative. This is a new discovery of explosive synchronization transitions in weighted complex networks, which provides a fresh angle and tool to understand this explosive behavior.

Explosive synchronization in weighted complex networks

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and nonlinear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.

Structural Robustness of Weighted Complex Networks Based on Natural Connectivity

Natural connectivity has been recently proposed to efficiently characterize the structural robustness of complex networks. The natural connectivity, interpreted as the Helmholtz free energy of a network, can be derived from the graph spectrum. We extend the concept of natural connectivity to weighted complex networks, in which the weight represents the number of multiple edges. We prove that the weighted natural connectivity changes monotonically when the weights are increased or decreased. We investigate the influence of weight on the network robustness within scenarios of weight changing and show that the weighted natural connectivity allows a precise quantitative analysis of the structural robustness for weighted complex networks.

Detecting overlapping communities by seed community in weighted complex networks

Detection of community structures in the weighted complex networks is significant to understand the network structures and analysis of the network properties. We present a unique algorithm to detect overlapping communities in the weighted complex networks with considerable accuracy. For a given weighted network, all the seed communities are first extracted. Then to each seed community, more community members are absorbed using the absorbing degree function. In addition, our algorithm successfully finds common nodes between communities. The experiments using some real-world networks show that the performance of our algorithm is satisfactory.

Synchronization-based topology identification of uncertain stochastic delay complex networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

Topological Strata of Weighted Complex Networks.

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.

Dynamical robustness analysis of weighted complex networks

Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.

An LCOR model for suppressing cascading failure in weighted complex networks

Based on the relationship between capacity and load, cascading failure on weighted complex networks is investigated, and a load-capacity optimal relationship (LCOR) model is proposed in this paper. Compared with three other kinds of load-capacity linear or non-linear relationship models in model networks as well as a number of real-world weighted networks including the railway network, the airports network and the metro network, the LCOR model is shown to have the best robustness against cascading failure with less cost. Furthermore, theoretical analysis and computational method of its cost threshold are provided to validate the effectiveness of the LCOR model. The results show that the LCOR model is effective for designing real-world networks with high robustness and less cost against cascading failure.

Construction and Analysis of the Model of Energy Metabolism in E. coli

Genome-scale models of metabolism have only been analyzed with the constraint-based modelling philosophy and there have been several genome-scale gene-protein-reaction models. But research on the modelling for energy metabolism of organisms just began in recent years and research on metabolic weighted complex network are rare in literature. We have made three research based on the complete model of E. coli’s energy metabolism. We first constructed a metabolic weighted network using the rates of free energy consumption within metabolic reactions as the weights. We then analyzed some structural characters of the metabolic weighted network that we constructed. We found that the distribution of the weight values was uneven, that most of the weight values were zero while reactions with abstract large weight values were rare and that the relationship between w (weight values) and v (flux values) was not of linear correlation. At last, we have done some research on the equilibrium of free energy for the energy metabolism system of E. coli. We found that (free energy rate input from the environment) can meet the demand of (free energy rate dissipated by chemical process) and that chemical process plays a great role in the dissipation of free energy in cells. By these research and to a certain extend, we can understand more about the energy metabolism of E. coli.

Weighted Complex Network Analysis of Pakistan Highways

The structure and properties of public transportation networks have great implications in urban planning, public policies, and infectious disease control. This study contributes a weighted complex network analysis of travel routes on the national highway network of Pakistan. The network is responsible for handling 75 percent of the road traffic yet is largely inadequate, poor, and unreliable. The highway network displays small world properties and is assortative in nature. Based on the betweenness centrality of the nodes, the most important cities are identified as this could help in identifying the potential congestion points in the network. Keeping in view the strategic location of Pakistan, such a study is of practical importance and could provide opportunities for policy makers to improve the performance of the highway network.

Scaling of average sending time on weighted Koch networks

Random walks on weighted complex networks, especially scale-free networks, have attracted considerable interest in the past. But the efficiency of a hub sending information on scale-free small-world networks has been addressed less. In this paper, we study random walks on a class of weighted Koch networks with scaling factor 0 &amp;lt; r ⩽ 1. We derive some basic properties for random walks on the weighted Koch networks, based on which we calculate analytically the average sending time (AST) defined as the average of mean first-passage times (MFPTs) from a hub node to all other nodes, excluding the hub itself. The obtained result displays that for 0 &amp;lt; r &amp;lt; 1 in large networks the AST grows as a power-law function of the network order with the exponent, represented by \documentclass[12pt]{minimal}\begin{document}$\log _{4}\frac{3r+1}{r}$\end{document}log43r+1r, and for r = 1 in large networks the AST grows with network order as N ln N, which is larger than the linear scaling of the average receiving time defined as the average of MFPTs for random walks to a given hub node averaged over all starting points.

Distributed flow optimization and cascading effects in weighted complex networks

We investigate the effect of a specific edge weighting scheme ~(k i k j )β on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter β and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we explore the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter β, we find that network resilience to cascading overloads and network throughput is optimal for the same value of β over the range of node capacities and available bandwidth.

On Global Adaptive Synchronization in Weighted Complex Networks

Pinning adaptive synchronization is investigated in weighted complex networks and several criteria are obtained for globally exponentially asymptotic synchronization. The number of pinned nodes can be obtained by calculating the eigenvalue of the minor matrix of an extended coupling matrix. Especially, pinning adaptive controllers are rather simple compared with some traditional controllers. Specifically and randomly pinning schemes are considered. When the network Control Rank information is known, the specifically pinning scheme of the most highly connected nodes is shown to require a significantly smaller number of local controllers when compared with the randomly pinning scheme. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria in weighted dynamical networks.

Remotely Sensed Image Classification by Complex Network Eigenvalue and Connected Degree

It is a well-known problem of remotely sensed images classification due to its complexity. This paper proposes a remotely sensed image classification method based on weighted complex network clustering using the traditional K-means clustering algorithm. First, the degree of complex network and clustering coefficient of weighted feature are used to extract the features of the remote sensing image. Then, the integrated features of remote sensing image are combined to be used as the basis of classification. Finally, K-means algorithm is used to classify the remotely sensed images. The advantage of the proposed classification method lies in obtaining better clustering centers. The experimental results show that the proposed method gives an increase of 8% in accuracy compared with the traditional K-means algorithm and the Iterative Self-Organizing Data Analysis Technique (ISODATA) algorithm.

Analysis of community evaluation criterion and discovery algorithm of weighted complex network

The clustering of nodes is an important feature of complex network. Previous researches mainly focus on community discovery in unweighted network, with little attention paid to the weighted network because of the complexity of weighted network. The community discovery of the weighted network is believed to be a much more difficult task. In this paper, we perform a study on the effectivenesses of community evaluation criterion and the performances of the existing discovery algorithms. First, we summarize three classical community evaluation criterions of weighted network, and analyze their effectivenesses according to a simulated noisy dataset, which has different community sizes, densities and local characteristics. Second, we adopt five datasets to compare the performances of three typical community discovery algorithms. The study shows that the existing criterions encounter difficulties in evaluating the basic community structure and in evaluating the weighted community with complex structure, and the generalization ability of the typical community discovery algorithm of weighted network is unsatisfactory.

Keyword Extraction of Document Based on Weighted Complex Network

This document explains and demonstrates how to extract keyword from Chinese document based on weighted complex network. The characteristic and disadvantages of several common automatic keyword extraction methods are introduced firstly. Then based on the ideas of complex network, we proposed an improved automatic keyword extraction method. Using complex network, a Chinese document is first represented as a network: the node represents the term, and the edge represents the Co-Occurrence of terms. Then we calculate the integrate value of each term, the keywords are top k terms with greatest value. The experiment results show that the method is more effective and accurate in comparison with the traditional method TFIDF keyword extraction from the same document.