Characteristics Of Complex Networks Research Articles

Investigation on structural and spatial characteristics of taxi trip trajectory network in Xi’an, China

An urban taxi transport network provides convenience for urban residents, and is also an important part of interconnecting suburbs and inner cities. Based on the GPS trajectory data of 14, 139 taxis, a kind of urban trip complex network was constructed. The clustering coefficient, average shortest path, vertex intensity, network density, K-core and other indexes that reflect the complex network characteristics of the taxis were studied, and the topological properties and geographical characteristics were analyzed. Xi’an’s taxi transport network has small-world characteristics and group characteristics, and that the average taxi trip is mainly 5.756 km. Distribution of vertex intensity in the traffic zones (minimum spatial analysis unit of transport network study) of the taxi network is uneven, which presents “fewer vertexes in large zones but more in the small ones, ” characteristic. The traffic zones with high cohesion are shaped as British Union Jack. Obviously, the research results indicate the interaction relationship between the topology structure and spatial differentiation of taxi trip trajectory network, and reveals urban resident activities’ spatial characteristics, movement rules and the mutual influence of urban functions’ spatial layout and resident activities, which may serve as references for those trying to optimize the taxi transport network and taxi operation management.

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

The investigation of the hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.

Anomaly Detection of Complex Networks Based on Intuitionistic Fuzzy Set Ensemble**Supported by the National Natural Science Foundation of China under Grant No 61671142, and the Fundamental Research Funds for the Central Universities under Grant No 02190022117021.

Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set (IFS)-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks. Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership, non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.

Efficient weighting strategy for enhancing synchronizability of complex networks

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

A Complex Network Methodology for Travel Demand Model Evaluation and Validation

Travel demand can be viewed as a weighted and directed graph where nodes are the origins and destinations and links represent the trips between nodes. This paper presents a network-theoretic methodology to evaluate and validate travel demand models. We apply the proposed method on three disaggregate travel demand models from Melbourne, Australia. Statistical properties of the modeled networks are compared against the observed networks over time. The new approach reveals the network structure and connectivity of the modeled trips that are not usually captured by traditional evaluation and validation methods. Results demonstrate the complexity involved in the development, evaluation, and validation of travel demand models, which calls for advanced evaluation techniques reflecting a wide range of attributes of the observed and modeled data, travelers, mobility patterns, and complex network characteristics.

OLCPM: An online framework for detecting overlapping communities in dynamic social networks

Community structure is one of the most prominent features of complex networks. Community structure detection is of great importance to provide insights into the network structure and functionalities. Most proposals focus on static networks. However, finding communities in a dynamic network is even more challenging, especially when communities overlap with each other. In this article, we present an online algorithm, called OLCPM, based on clique percolation and label propagation methods. OLCPM can detect overlapping communities and works on temporal networks with a fine granularity. By locally updating the community structure, OLCPM delivers significant improvement in running time compared with previous clique percolation techniques. The experimental results on both synthetic and real-world networks illustrate the effectiveness of the method.

Exploration of polygons in online social networks

Online social networks have continued to attract increased attention since the introduction of this concept nearly three decades ago. Consequently, a study about the workings of online social networks may help in understanding the structure of human society and the characteristics of generic complex networks. Over the past few years, interest in neighboring nodes, which are the number of nodes between any two nodes, the number of neighbors and how many triangles are present in a social network have produced the concepts of a six-degree separation (Milgram, Psychol Today 2(1):60–67, 1967; Backstrom et al., Proceedings of the 4th annual ACM web science conference, p 33–42, 2012), a heavy tail in the degree distribution (Barabasi, Albert, Science 286(5439):509–512, 1999) and a high clustering coefficient (Luce, Perry, Psychometrika 14(2):95–116, 1949; Watts, Strogatz, Nature 393(6684):440–442, 1998; Amaral et al., Proc Natl Acad Sci USA 97(21):11149–11152, 2000). In a similar manner, researchers have also been curious about how many polygons are present in a given online social network. Although much effort has been expended (Dantzig et al., International symposium on theory of graphs, p 77–83, 1967; Kamae, IEEE Trans Circuit Theory 14(2):166–171, 1967; Gotlieb, Corneil, Commun ACM 10(12):780–783, 1967; Welch, J ACM 13(2):205–210, 1966; Tiernan, Commun ACM 13(12):722–726, 1970; Tarjan, SIAM J Comput 2(3):211–216, 1973; Johnson, SIAM J Comput 4:77–84, 1975; Mateti, Deo, SIAM J Comput 5(5):90–99, 1976; Marinari et al., Europhys Lett 73(3):301–307, 2005), studying this subject, the inability to enumerate polygons has stymied an in depth understanding of the properties of polygons in an online social network. In the study described in this paper, the estimated number of polygons in an online social network is revealed. It was found that in the current widely used online social networks, e.g., Facebook, Twitter, the number of polygons increases drastically when the length of a polygon is below a set value and then it decreases rapidly. The average length of the network polygons was calculated and it was found that online social networks contain a relatively large average length of polygons. Based on this perspective, a massive labyrinth of polygons would make the online social networks appear to be very complicated. To further investigate this area, a generalized clustering coefficient was explored. Results showed that the generalized clustering coefficient appeared to descend exponentially with the length of polygon and expeditiously approached zero. This result suggested that the polygons with large lengths should be ignored in many scenarios. Since the polygons with lengths greater than five appeared to have little impact on the network, the online social networks appeared to be less complex than anticipated. The polygon is one of the fundamental problems in graph theory and complex networks, so that the work reported here may be beneficial for many disciplines, including transportation [7], engineering [8], computer science [9–16], physics (Birmele et al., Proceedings of the 24th annual ACM–SIAM symposium on discrete algorithms, p 1884–1896, 2013), sociology (Motter, Albert, Phys Today 65:43, 2012), epidemiology (Feld, Am J Sociol 96(6):1464–1477, 1991; Cohen et al., Phys Rev Lett 91(24):12343, 2002), psychology (Sun et al., Sci Rep 4(6188):5099–5099, 2014), biology (Feiler, Kleinbaum, Psychol Sci, 2015), medicine (Kincaid, Pilette, Comput Appl Biosci Cabios 8:267–273, 1992), geography (Kim et al., Lancet 386(9989):145–153, 2015), etc.

A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks

Identifying the most influential spreaders with the aim of reaching a maximum spreading ability has been a challenging and crucial topic so far. Many centrality measures have been proposed to identify the importance of nodes in spreader detection process. Centrality measures are used to rank the spreading power of nodes. These centralities belong to either local, semi-local, or global category. Local centralities have accuracy problem and global measures need a higher time complexity that are inefficient for large-scale networks. In contrast, semi-local measures are popular methods that have high accuracy and near-linear time complexity. In this paper, we have proposed a new semi-local and free-parameter centrality measure by applying the natural characteristics of complex networks. The proposed centrality can assign higher ranks for structural holes as better spreaders in the network. It uses the positive effects of second-level neighbors’ clustering coefficient and negative effects of node's clustering coefficient in defining the importance of nodes. Therefore, the proposed centrality avoids selection of spreaders that are too close to one another. We compare the proposed method with different centrality measures based on Susceptible–Infected–Recovered (SIR) and Susceptible–Infected (SI) models on both artificial and real-world networks. Experiments on both artificial and real networks show that our method has its competitive advantages over the other compared centralities.

Interest Points Detection in Image Based on Topology Features of Multi-level Complex Networks

In this paper, we presents a new method for extracting interest points from RGB images by complex network analysis theory. Firstly, the RGB images are expressed as the multi-level complex network model. The nodes in the complex network model are the maximum degree pixel of subgraphs and the links are the similarity and distance between the maximum degree pixels. Then three different algorithms were proposed to locate these interest points based on three topology features of high-level complex network model, which are degree, closeness and betweenness centrality. In order to verify the effectiveness of our algorithm, we use our algorithm for four different test images. It is remarkable that the identify targets by degree centrality algorithm are similar to Harris and SIFT algorithm, and the accuracy are more than them. The results show that our algorithm could identify interest points from the images effectively.

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

CRITIC-Based Node Importance Evaluation in Skeleton-Network Reconfiguration of Power Grids

Seven centrality indexes are first presented for identifying important nodes with topological features of a complex network and electrical characteristics of a power system considered. Then, a criteria importance through intercriteria correlation-based multi-index decision-making method, in which entropy and the Spearman’s rank correlation coefficient are integrated for reflecting the differences and correlations among multiple indexes, respectively, is presented to comprehensively identify the importance degrees of nodes in a given power grid. Finally, the proposed indexes and method are applied to actual Guangdong power system in China, and the results are compared with those attained by single-attribute and multi-attribute evaluation methods.

Using functional dependency and node closure to detect communities from the sparse network

Community structure is one of the most important features of complex networks, a large number of methods have been proposed to extract community structures from networks. However, some of those methods suffer from the high time complexity, and some of them cannot obtain the acceptable results. In this paper, we borrow the idea from the database theory, and propose the concepts of functional dependency (FD) between nodes and node closure first, then we utilize these concepts to extract communities. This method takes both effectiveness and efficiency into consideration, the community detection process can be accomplished with O(m) time consumption. We conducted extensive experiments both on some synthetic networks and on some real-world networks, the experimental results demonstrate that the method can detect communities from a given network successfully.

Software Vulnerability Prediction Models Based on Complex Network

Recently, the software has been developed increasingly. It is more and more difficult to find software vulnerabilities. Therefore, this paper proposes a software vulnerability prediction model based on the complex network. This model regards the software defect evaluation as three classifications or regression sub-problems, including the defects in each class, software defect severity evaluation and software defect priority evaluation. This model uses machine learning method to train complex network feature, object-oriented feature and structure feature. The model can evaluate software defects on the hierarchy of class and assess software vulnerability effectively. An experiment on Hibernate is carried out, which selects random forest model as each sub-model. The experiment shows that the model is valid and accurate to evaluate vulnerability.

Research on edges immunization strategy for complex network based on SIS-CA model

This paper proposes a targeted edges immunization strategy, which aims to immune a certain number of the most important edges from the perspective of protecting transmission path. To better simulate the dynamic changes of risks propagation in real complex networks, an SIS-CA (Susceptible-Infected-Susceptible Cellular Automation) propagation model is developed, which combines SIS (Susceptible-Infected-Susceptible) model with the cellular automata (CA) method and takes nonuniformity and adjustment time into consideration. Based on SIS-CA propagation model, the feasibility of targeted edges immunization strategy was analysed in comparison with other targeted immunization strategy in the WS (Watts-Strogatz) small-world network model, BA (Barabasi-Albert) scale-free network model, and an aircraft manufacturing enterprise collaboration network (MECN) known to have the features of complex networks. The test results show that compared with conventional targeted immunization strategies, the proposed targeted edges immunization strategy obtains a better immunization efficacy via protecting fewer key edges.

Rational graph: a model for complex networks

Real life networks like social, biological and technical networks have amazing characteristics. These networks grow rapidly by the continuous addition of new nodes without following any organisation. Despite their huge sizes, these networks have a short path length, high clustering and power law degree distribution. Here, we investigate the topological characteristics of these types of networks. We also explore the main graph models that have been proposed to represent the dynamics and growth of these networks. This work provides an original contribution to build a complex network model. Motivated by the structural characteristics of complex networks and the deficiencies in the existing graph models, we are proposing the rational model, which is a model that imitates the characteristics of complex networks. The model was implemented and examined against other complex network models. The results showed that the rational model imitates the growth behaviour of the network, while maintaining the expected topological properties of the network.

Security Feature Measurement for Frequent Dynamic Execution Paths in Software System

The scale and complexity of software systems are constantly increasing, imposing new challenges for software fault location and daily maintenance. In this paper, the Security Feature measurement algorithm of Frequent dynamic execution Paths in Software, SFFPS, is proposed to provide a basis for improving the security and reliability of software. First, the dynamic execution of a complex software system is mapped onto a complex network model and sequence model. This, combined with the invocation and dependency relationships between function nodes, fault cumulative effect, and spread effect, can be analyzed. The function node security features of the software complex network are defined and measured according to the degree distribution and global step attenuation factor. Finally, frequent software execution paths are mined and weighted, and security metrics of the frequent paths are obtained and sorted. The experimental results show that SFFPS has good time performance and scalability, and the security features of the important paths in the software can be effectively measured. This study provides a guide for the research of defect propagation, software reliability, and software integration testing.

Network structure optimization algorithm for information propagation considering edge clustering and diffusion characteristics

Optimizing network structure to promote information propagation has been a key issue in the research field of complex network, and both clustering and diffusion characteristics of edges in a network play a very important role in information propagation. K-truss decomposition is an algorithm for identifying the most influential nodes in the network. We find that K-truss decomposition only considers edge clustering characteristics, without considering the diffusion characteristics, so it is easily affected by the local clustering structure in the network, such as core-like groups. There are mutually closely connected the core-like groups in the network, but the correlation between the core-like groups and the other parts of the network is less, so the information is easy to spread in the core-like groups, but not in the other parts of the network, nor over the whole network. For the reason, we propose an index to measure the edge diffusion characteristics in a network, and it is found that the diffusion characteristics of some edges in the periphery of the network are relatively high, but the clustering characteristics of these edges are relatively low, so they are not beneficial for rapid information propagation. In this paper, by considering the relationship between the clustering characteristics and diffusion characteristics of the edges, we propose a novel network structure optimization algorithm for information propagation. By measuring the comprehensive ability strength of the clustering characteristics and the diffusion characteristics of the edges, we can filter out the edges whose comprehensive ability is poor in the network, then determine whether the edges should be optimized according to the relative relationship between the clustering characteristics and the diffusion characteristics of the edges. To prove the effectiveness of the proposed algorithm, it is carried out to optimize the structures of four real networks, and verify the effective range of information propagation before and after the optimization of network structure from the classical independent cascade model. The results show that the network topology optimized by the proposed algorithm can effectively increase the range of information propagation. Moreover, the number of leaf nodes in the optimized network is reduced, and the clustering coefficient and the average path length are also reduced.

A New Modelling and Feature Extraction Method Based on Complex Network and Its Application in Machine Fault Diagnosis

The application of the existing complex network in fault diagnosis is usually modelled based on the time domain, resulting in the loss of sign frequency‐domain features, and the extracted topology features of network are too macroscopic and insensitive to local changes within the network. This paper proposes a new method of local feature extraction based on frequency complex network (FCN) decomposition and builds a new complex network structure feature on this basis, namely, subnetwork average degree. The variation law of signals in frequency domain is obtained with the aid of the structural features of complex network. The local features that are sensitive to local changes of the network are applied to characterize the whole network, with flexible application and without limitation in mechanism. The average degree of subnetwork could be regarded as feature parameters for rolling bearing fault diagnosis and degradation state recognition. Analysis on the experimental data and bearing life cycle data shows that the method proposed in this paper is effective, revealing that the extracted features have effective separability and high accuracy in fault recognition and the degradation detection of the life cycle of rolling bearings combined with neural networks. Moreover, the proposed method has reference value for the processing and recognition of other nonstationary signals.

Comparative Study Of Complex Network Community Structure Algorithms In network Pharmacology Analysis

Community structure is an extremely important characteristic of complex networks composed of network pharmacology. The mining of network community structure is of great importance in many fields such as biology, computer science and sociology. In recent years, for different types of large-scale complex networks, researchers had proposed many algorithms for finding community structures. This paper reviewed some of the most representative algorithms in the field of network pharmacology, and focused on the analysis of the improved algorithms based on the modularity index and the new algorithms that could reflect the level and overlap of the community. Finally, a benchmark was established to measure the quality of the community classification algorithm.

Structure Characteristics Analysis of Diesel Sales in Complex Network Method

With the rising profits of oil companies in the refined oil sector, the optimization of the refined oil supply chain network has received more and more attention. In most supply chains (SCs), transaction relationships between suppliers and customers are commonly considered to be an extrapolation from a linear perspective. However, this traditional linear concept of an SC is egotistic and oversimplified and does not sufficiently reflect the complex and structure of supplier–customer relationships in current economic and industrial situations. But key global knowledge can be obtained from complex network characteristics analysis of the net form sales system. For two-level network like refine oil supply network, this paper proposed an integrated framework to explore its characteristics. Through various analyses of this complex network, including visual, network scale, network agglomeration, network community and geographic information analyses, we could found the characteristics of regular network node relations and regional location characteristics, as well as a strongly correlation between correlation coefficient thresholds and the network interdependence, and also moderated the correlation between SN efficiency and SN resilience. In order to testify this supply network analysis method, we conducted a real-world SN analyses based on a Chinese province diesel supply network and describe an advanced investigation of SN theory. This method enrich the SN theory, which can benefit SN management, community economics and industrial resilience. Also the basic understanding of the diesel sales network system obtained in this paper provides guidance for further research on this network structure, which can also provide a reference for regional sales supervision and resource distribution.