Complex Network Research Research Articles

The accumulative law and its probability model: an extension of the Pareto distribution and the log-normal distribution.

The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains.

Enhancing robustness of link prediction for noisy complex networks

In recent years, complex networks research have attracted considerable attention, in which link prediction has been taken as an effective tool for predicting missing links or identifying spurious links from available datasets. In reality, the collected networks are always noisy and represent patterns of measured structure, not the true structure of complex systems. However, most of the existing link prediction methods have been developed based on the assumption that the observed networks are reliable. Therefore, how to strengthen the robustness of link prediction methods thereby improving prediction accuracy in noisy networks becomes an important problem. In this paper, we propose a novel link prediction method which combines low-rank representation and non-negative matrix factorization for similarity matrix calculation. The low-rank module decomposes the adjacent matrix of networks into a low rank backbone structure and a sparse noise matrix, and the matrix factorization module characterizes the structural patterns of networks comprehensively with multiple perturbation mechanism. The idea behind the method is that we reshape the original network through the addition and deletion of some links identified by low-rank modeling, thus the important parts of the original network are emphasized. Based on the exaggerated but characteristic network, the potential links may be predicted more accurately. Experimental results on synthetic and real-world networks demonstrate that the proposed method performs better than state-of-the-art methods for link prediction in noisy networks.

Research on complex network community identification based on partially optimized genetic algorithm

The research of complex networks has become a hot research field, and has been successfully applied in many fields such as social network analysis, protein network analysis, and link prediction. In this paper, the traditional genetic algorithm has strong randomness and weak search ability in the co mmunity identification method. A complex network community recognition algorithm based on local optimization genetic algorithm is proposed. The method uses label propagation strategy to produce a certain precision. The initial population; a combined one-way crossover strategy is proposed to avoid destroying the original excellent community structure in the cross process; the local heuristic mutation strategy is used to ensure the accuracy of the identification community, and the overall optimization ability of the algorithm is realized. Finally, the effectiveness of the algorithm is verified by experiments.

Evolution of spatial structure patterns of city networks in the Yangtze River Economic Belt from the perspective of corporate pledge linkage

AbstractThe pledge of stock rights is a method for measuring the external horizontal connections of enterprises, which is more suitable to represent the city network compared with the vertical connections of enterprises. Meanwhile, it is greatly significant to express the relationships of regional spaces. The paper characterizes and explores the evolution of urban spatial structure with complex network research methods to enrich the relevant works on city networks in the Yangtze River Economic Belt from 2011 to 2017. The results are as follows: First, from 2011 to 2017, the pledge of stock rights among cities was enhanced significantly, and the trend of the city networks' characteristics become strengthened and more complicated. Second, cities in the Yangtze River Delta have relatively high connection values, however, cities in the western area are holding peripheral positions within the city network. Third, due to the advantages of economic agglomeration and radiation, the provincial capital have become the core nodes in the city network. Fourth, Shanghai, Hangzhou, and Nanjing have dominant positions within city networks in the Yangtze River Economic Belt. Particularly, Shanghai, as one of the leading financial centers in China, has a growing influence on other cities and gradually evolved into a regional growth pole city and the first core city.

SCRN: A Complex Network Reconstruction Method Based on Multiple Time Series

Complex network reconfiguration has always been an important task in complex network research. Simple and effective complex network reconstruction methods can promote the understanding of the operation of complex systems in the real world. There are many complex systems, such as stock systems, social systems and thermal power systems. These systems generally produce correlated time series of data. Discovering the relationships among these multivariate time series is the focus of this research. This paper proposes a Spearman coefficient reconstruction network (SCRN) method based on the Spearman correlation coefficient. In the SCRN method, we select entities in the real world as the nodes of the network and determine connection weights of the network edges by calculating the Spearman correlation coefficients among nodes. In this paper, we selected a stock system and boiler equipment in a thermal power generation system to construct two complex network models. For the stock network model, we used the classic Girvan–Newman (GN) algorithm for community discovery to determine whether the proposed network topology is reasonable. For the boiler network model, we built a predictive model based on an support vector regression (SVR) model in machine learning, and we verified the rationality of the boiler model by predicting the amount of boiler steam.

Influencers Identification in Weighted and Directed Networks Based on k-layer Decomposition

In recent years, complex network research has received wide attention from scientific and industrial circles in different academic fields owing to its high application value. In the field of complex network research, identifying influencers has far-reaching implications for various real-world propagation dynamics, such as epidemic outbreaks, and cascading failures. In this paper, we analyse the node-specific attributes of weighted and directed networks and propose two new influencers identification indices for weighted and directed networks. For weighted networks, in k-layer decomposition, weighted degree is used in the algorithm instead of degree as the basis for decomposition. For directed networks, we separately consider the effect of in-degree and out-degree on network decomposition and propose directed k-layer (KLD) indicators that are more suitable for directed networks. Thereafter, a Susceptible-Infected-Recovered (SIR) model and network robustness evaluation methods are used to compare and evaluate the proposed indices on multiple real-world complex network datasets. We found that using the proposed indices resulted in improved node ranking ability for weighted or directed networks.

A Complex Network Model for Analysis of Fractured Rock Permeability

Fractured rocks exist widely in nature. The fracture network is an effective storage space and main seepage channel of low‐permeability oil and gas reservoirs, which controls the seepage system of low‐permeability oil and gas reservoirs. The connection characteristics of fracture networks are complex and evolve dynamically with time. The rise of complex network research can provide reliable analysis for the relationship between network structures and network behaviors. In this work, the fracture network is considered as a hierarchical network with self‐similarity, and complex network theory is applied to analyze the permeability of fractured rocks. According to the power‐law relationship of degree distribution of network nodes, the number of nodes is corresponding to the number of network edges and a new power‐law distribution relationship of edges with degree of nodes is proposed. Eventually, the permeability model of fractured rocks is derived and it is found that permeability of fractured rocks is a function of degree of maximum node kmax, self‐similarity index γ, power index dk, and other structural parameters. Compared with the existing numerical simulations, the validity of the model is verified. By calculating the influence of model parameters on the permeability, the following results are obtained: (1) fracture porosity is directly proportional to permeability; (2) fracture surface density is linearly increasing with permeability; (3) power index is inversely proportional to permeability; and (4) permeability is exponentially increasing with the maximum degree of a node.

Analyses and applications of optimization methods for complex network reconstruction

Inferring the topology of a network from observable dynamics is a key topic in the research of complex network. With the observation error considered, the topology inferring is formulated as a connectivity reconstruction problem that can be solved through optimization estimation. It is found that the different optimization methods should be selected to deal with the different degrees of noise, different scales of observable time series and such other situations when it comes to the problem of connectivity reconstruction, which has not been analyzed and discussed before yet. In this paper, four regression methods, namely least squares, ridge, lasso and elastic net, are used to solve the problem of network reconstruction in different situations. In particular, a further analysis is made of the effects of each regression method on the network reconstruction problem in detail. Through simulation of a variety of artificial and real networks, as it has turned out, the four regression methods are effective in respect to network reconstruction when certain conditions are respectively satisfied. Based on the experimental results, it is possible to reach some interesting conclusions that can guide our readers to know the internal mechanisms for network reconstruction and choose the appropriate regression method in accordance with the actual situation and existing knowledge.

The Complexity of the Homeopathic Healing Response Part 1: The Role of the Body as a Complex Adaptive System in Simillimum-Initiated Recovery from Disease.

The concepts of complex systems science enhance the understanding of how people develop and recover from disease. Living systems (human beings, animals, and plants) are self-organizing complex adaptive systems (CAS): that is, interconnected networks. CAS maintain life by initiating and carrying out non-linear dynamical changes to optimize survival fitness and function in the context of an ever-changing environment. In Part 1 of this two-part paper, we relate concepts from complex systems science to homeopathic healing. The systemic changes of homeopathic healing involve adaptive patterns of responses to salient signals (similia) for reversing disease patterns and generating emergent multi-symptom healing over time. This narrative review relates homeopathic clinical practice theory to complex systems and network research. Homeopathic medicines communicate individually salient environmental information to the organism, with effects that are multi-system and indirect. The body's defense mechanisms recognize the self-similar information that the correctly chosen simillimum medicine at low dose conveys as a weak external/internal environmental stressor or danger signal (hormetin) to mobilize neural and cellular defenses. The body networks then use endogenous cell to cell signaling and amplify the small magnitude signal information. The results are disproportionately large: that is, non-linear, adaptive, modifications across the inter-connected self-organized biological networks/sub-systems of the body. CAS amplification mechanisms for small or weak signals include stochastic resonance, time-dependent sensitization, and hormesis. The body as a complex system has the capacity for self-organization, emergence and self-similarity over global (overall health and wellbeing) and local (organ) levels of organization. These features are key for future research on the systemic healing that evolves over time during individualized homeopathic treatment.

An overlapping community detection algorithm based on node distance of line graph

Overlapping community detection is a hot topic in research of complex networks. Link community detection is a popular approach to discover overlapping communities. Line graph is a widely used model in link community detection. In this paper, we propose an overlapping community detection algorithm based on node distance of line graph. Considering topological structure of links in graphs, we use line graph to transform links of graph into nodes of line graph. Then, we calculate node distance of line graph according to their dissimilarity. After getting distance matrix, we proposed a new [Formula: see text] measure based on nodes of line graph and combine it with clustering algorithm by fast search and density peak to identify node communities of line graph. Finally, we acquire overlapping node communities after transforming node communities of line graph back to graph. The experimental results show that our algorithm achieves a higher performance on normalized mutual information metric.

Locating the Epidemic Source in Complex Networks with Sparse Observers

Epidemic source localization is one of the most meaningful areas of research in complex networks, which helps solve the problem of infectious disease spread. Limited by incomplete information of nodes and inevitable randomness of the spread process, locating the epidemic source becomes a little difficult. In this paper, we propose an efficient algorithm via Bayesian Estimation to locate the epidemic source and find the initial time in complex networks with sparse observers. By modeling the infected time of observers, we put forward a valid epidemic source localization method for tree network and further extend it to the general network via maximum spanning tree. The numerical analyses in synthetic networks and empirical networks show that our algorithm has a higher source localization accuracy than other comparison algorithms. In particular, when the randomness of the spread path enhances, our algorithm has a better performance. We believe that our method can provide an effective reference for epidemic spread and source localization in complex networks.

WSBP/NWBP small-world neural network and its performance for wind power forecasting

A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks. This paper presents two novel small-world neural networks, the Watts-Strogatz small-world based on a BP neural network (WSBP) and a Newman-Watts small-world neural network based on a BP neural network (NWBP), related to previous research of complex networks. The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures, and their derivation and convergence criterion are progressively discussed. After that, the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms. Finally, a wind power prediction system is advanced to verify their generalization abilities, and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.

How to predict social relationships — Physics-inspired approach to link prediction

Link prediction in social networks has a long history in complex network research area. The formation of links in networks has been approached by scientists from different backgrounds, ranging from physics to computer science. To predict the formation of new links, we consider measures which originate from network science and use them in the place of mass and distance within the formalism of Newton’s Gravitational Law. The attraction force calculated in this way is treated as a proxy for the likelihood of link formation. In particular, we use three different measures of vertex centrality as mass, and 13 dissimilarity measures including shortest path and inverse Katz score in place of distance, leading to over 50 combinations that we evaluate empirically. Combining these through gravitational law allows us to couple popularity with similarity, two important characteristics for link prediction in social networks. Performance of our predictors is evaluated using Area Under the Precision–Recall Curve (AUC) for seven different real-world network datasets. The experiments demonstrate that this approach tends to outperform the setting in which vertex similarity measures like Katz are used on their own. Our approach also gives us the opportunity to combine network’s global and local properties for predicting future or missing links. Our study shows that the use of the physical law which combines node importance with measures quantifying how distant the nodes are, is a promising research direction in social link prediction.

Measuring Software Modularity Based on Software Networks.

Modularity has been regarded as one of the most important properties of a successful software design. It has significant impact on many external quality attributes such as reusability, maintainability, and understandability. Thus, proposing metrics to measure the software modularity can be very useful. Although several metrics have been proposed to characterize some modularity-related attributes, they fail to characterize software modularity as a whole. A complex network uses network models to abstract the internal structure of complex systems, providing a general way to analyze complex systems as a whole. In this paper, we introduce the complex network theory into software engineering and employ modularity, a metric widely used in the field of community detection in complex network research, to measure software modularity as a whole. First, a specific piece of software is represented by a software network, feature coupling network (FCN), where methods and attributes are nodes, couplings between methods and attributes are edges, and the weight on the edges denotes the coupling strength. Then, modularity is applied to the FCN to measure software modularity. We apply the Weyuker’s criteria which is widely used in the field of software metrics, to validate the modularity as a software metric theoretically, and also perform an empirical evaluation using open-source Java software systems to show its effectiveness as a software metric to measure software modularity.

Binary opinion dynamics on signed networks based on Ising model

The evolution dynamics of public opinion is a hot issue in complex networks research. And the Ising model is the earliest classic dynamic model of public opinion. Although signed networks can describe amicable and antagonistic relationship in complex real-world systems accurately, and the research on dynamic process of public opinion evolution on signed networks is valuable, few people have paid attention to that. Previous methods for opinion diffusion cannot be applied to signed network directly, which ignore the important information contained in the negative edges. In this paper, the binary opinion dynamics on signed networks has been modeled by aid of the Ising model. The model is applied both to the synthetic and real-world signed networks. We observe that the proportion and distribution of negative edges have a fundamental effect on the evolutionary result of public opinion on signed networks. There exists the critical ratio. When the proportion of negative edges in the network exceeds the critical ratio, there appears to be a completely different evolutionary result, and the distribution of negative edges affects the value of the critical ratio. In addition, we study the network structural balance in the evolutionary process of opinion on signed networks as complementary. Our findings can deepen the understanding of the evolutionary process of binary opinion in real signed social systems.

Three-dimensional drivable optrode array for high-resolution neural stimulations and recordings in multiple brain regions

The brain-computer interface (BCI) devices are of prime important for study of nervous system as well as diagnosis and treatment of neurological disorders. To meet the needs of the BCI devices in high-density integration and multi-functionalization, 3-dimensional (3D) drivable optrode array with laser diodes (LDs) coupled waveguides was developed. The unique device realizes the 3D integration of the optrodes and avoids fiber tangle and tissue heating by adopting LD coupled waveguide structure. Besides, the postoperative position adjustment of the optrode array was achieved by integrating with a 3D printed micro-drive. Most importantly, high-resolution neural stimulations and recordings were achieved for study of working memory related neural circuits in four brain regions of mice including prelimbic cortex (PrL), mediodorsal thalamic nucleus (MD), dorsal medial caudate nucleus (dmCP) and posterior motor cortex 2 (pM2). The results indicate that this novel device is promising for the research of complex neural networks.

Multiple phase transitions in networks of directed networks

The robustness in real-world complex systems with dependency connectivities differs from that in isolated networks. Although most complex network research has focused on interdependent undirected systems, many real-world networks-such as gene regulatory networks and traffic networks-are directed. We thus develop an analytical framework for examining the robustness of networks made up of directed networks of differing topologies. We use it to predict the phase transitions that occur during node failures and to generate the phase diagrams of a number of different systems, including treelike and random regular (RR) networks of directed Erdős-Rényi (ER) networks and scale-free networks. We find that the the phase transition and phase diagram of networks of directed networks differ from those of networks of undirected networks. For example, the RR networks of directed ER networks show a hybrid phase transition that does not occur in networks of undirected ER networks. In addition, system robustness is affected by network topology in networks of directed networks. As coupling strength q increases, treelike networks of directed ER networks change from a second-order phase transition to a first-order phase transition, and RR networks of directed ER networks change from a second-order phase transition to a hybrid phase transition, then to a first-order phase transition, and finally to a region of collapse. We also find that heterogenous network systems are more robust than homogeneous network systems. We note that there are multiple phase transitions and triple points in the phase diagram of RR networks of directed networks and this helps us understand how to increase network robustness when designing interdependent infrastructure systems.

Modeling memetics using edge diversity

The study of meme propagation and the prediction of meme trajectory are emerging areas of interest in the field of complex networks research. In addition to the properties of the meme itself, the structural properties of the underlying network decides the speed and the trajectory of the propagating meme. In this paper, we provide an artificial framework for studying the meme propagation patterns. Firstly, the framework includes a synthetic network which simulates a real world network and acts as a testbed for meme simulation. Secondly, we propose a meme spreading model based on the diversity of edges in the network. Through the experiments conducted, we show that the generated synthetic network combined with the proposed spreading model is able to simulate a real world meme spread. Our proposed model is validated by the propagation of the Higgs boson meme on Twitter as well as many real world social networks.

Establishment and Analysis of the Supernetwork Model for Nanjing Metro Transportation System

In recent years, many researchers have applied complex network theory to urban public transport network to construct complex network and analyze its network performance. The original analysis method generally uses the Space L and Space R model to establish a simple link between public sites but ignores the organic link between the overall network system and the line subsystem. As an important part of urban public transport system, subway plays an important role in alleviating traffic pressure. In this paper, a supernetwork model of Nanjing metro network is established by using the supernetwork method. Three parameters, node-hyperedge degree, hyperedge-node degree, and hyperedge degree, are proposed to describe the model. The model is compared with the traditional Space L and Space P models. The study on the supernetwork model of Nanjing metro complex network shows that the network density, network centrality, and network clustering coefficient are large, and the average network distance is small, which meets the requirements of traffic planning and design. In this study, the subway line is considered as a subsystem and further simplified as a node, so that the complex network analysis method can be applied to the new supernetwork model, expanding the thinking of complex network research.

STUDY ON SYNCHRONIZATION STABILITY OF COMPLEX NETWORKS BASED ON IMPULSE CONTROL THEORY

A complex network is a complex set composed of several elementary units which have certain characteristics and functions and interact with each other. In recent years, the complex network has become one of the research hotspots of nonlinear science. Many scholars in the fields of control, mathematics, computer, biology and economy have devoted themselves to the research of complex networks. This study focuses on the stability of pinning impulse synchronization for the directed complex dynamic networks. From the Impulse Control Theory, a simple and general synchronization criterion for complex dynamic networks is obtained. Furthermore, the obtained results are applied to a small-world network consisting of a convolution neural network (CNN) and a Hodgkin-Huxley model neuron oscillator as power nodes. The numerical simulation shows the correctness of the obtained theoretical results and the validity of the control method.