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Link prediction is a significant and fundamental research issue in the field of network science. Numerous similarity-based algorithms have been widely applied due to low computational cost and high prediction accuracy. The topological features of networks like community structure are beneficial to link prediction. In this paper, we first introduce a Weighted Two-level Neighborhood Similarity (WTNS) index that integrates the resource allocation index and local path index. Then we define the Strength of Community Link (SCL) as a quantitative index to evaluate the close relationship among communities. Based on this, the connection likelihood between two nodes can be calculated and a new link prediction algorithm called SCL-WTNS is presented. The proposed algorithm has been compared with nine popular similarity methods on 12 real-world networks to verify the performance. SCL-WTNS is also compared with two groups of community-based link prediction methods. Experiments indicate that the proposed algorithm is better than comparison algorithms both in prediction accuracy and stability. [ABSTRACT FROM AUTHOR]

In this paper, the exact solutions of the logarithmic nonlinear Schrödinger equation (log-NLS) types, namely, the logarithmic perturbed nonlinear Schrödinger equation (log-pert-NLS), logarithmic improved nonlinear Schrödinger (log-imp-NLS) and logarithmic perturbed improved nonlinear Schrödinger (log-pert-imp-NLS) are examined. These solutions are attained by eliminating logarithmic nonlinearity. The solutions show different Gaussian solitary patterns in different conditions. The dynamics of the obtained solutions are analyzed by means of two-dimensional (2D) and three-dimensional (3D) graphs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problems of identifying the most appropriate model for a given physical system and of assessing the model contribution to the measurement uncertainty. The above problems are studied in terms of Bayesian model selection and model averaging. As the evaluation of the 'evidence' , i.e., the integral of Likelihood × Prior over the space of the measurand and the parameters, becomes impracticable when this space has dimensions, it is necessary to consider an appropriate numerical strategy. Among the many algorithms for calculating , we have investigated the ellipsoidal nested sampling, which is a technique based on three pillars: The study of the iso-likelihood contour lines of the integrand, a probabilistic estimate of the volume of the parameter space contained within the iso-likelihood contours and the random samplings from hyperellipsoids embedded in the integration variables. This paper lays out the essential ideas of this approach. [ABSTRACT FROM AUTHOR]

Recent years have witnessed the increasing of available network data; however, much of those data is incomplete. Link prediction, which can find the missing links of a network, plays an important role in the research and analysis of complex networks. Based on the assumption that two unconnected nodes which are highly similar are very likely to have an interaction, most of the existing algorithms solve the link prediction problem by computing nodes' similarities. The fundamental requirement of those algorithms is accurate and effective similarity indices. In this paper, we propose a new similarity index, namely similarity based on activity and connectivity (SAC), which performs link prediction more accurately. To compute the similarity between two nodes, this index employs the average activity of these two nodes in their common neighborhood and the connectivities between them and their common neighbors. The higher the average activity is and the stronger the connectivities are, the more similar the two nodes are. The proposed index not only commendably distinguishes the contributions of paths but also incorporates the influence of endpoints. Therefore, it can achieve a better predicting result. To verify the performance of SAC, we conduct experiments on 10 real-world networks. Experimental results demonstrate that SAC outperforms the compared baselines. [ABSTRACT FROM AUTHOR]

Label propagation algorithm (LPA) has been proven to be an extremely fast method for community detection in large complex networks. But an important issue of the algorithm has not yet been properly addressed that random update orders in label propagation process hamper the algorithm robustness of algorithm. We note that when there are multiple maximal labels among a node neighbors' labels, choosing a node' label from which there is a local cycle to the node instead of a random node' label can avoid the labels propagating among communities at random. In this paper, an improved LPA based on local cycles is given. We have evaluated the proposed algorithm on computer-generated networks with planted partition and some real-world networks whose community structure are already known. The result shows that the performance of the proposed approach is even significantly improved. [ABSTRACT FROM AUTHOR]

The label propagation algorithm (LPA) is a graph-based semi-supervised learning algorithm, which can predict the information of unlabeled nodes by a few of labeled nodes. It is a community detection method in the field of complex networks. This algorithm is easy to implement with low complexity and the effect is remarkable. It is widely applied in various fields. However, the randomness of the label propagation leads to the poor robustness of the algorithm, and the classification result is unstable. This paper proposes a LPA based on edge clustering coefficient. The node in the network selects a neighbor node whose edge clustering coefficient is the highest to update the label of node rather than a random neighbor node, so that we can effectively restrain the random spread of the label. The experimental results show that the LPA based on edge clustering coefficient has made improvement in the stability and accuracy of the algorithm. [ABSTRACT FROM AUTHOR]

Almost all existing approaches for community detection only make use of the network topology information, which completely ignore the background information of the network. However, in many real world applications, we may know some prior information that could be useful in detecting the community structures. Specifically, the true community assignments of certain nodes are known in advance. In this paper, a novel semi-supervised community detection approach is proposed based on label propagation, which can utilize prior information to guide the discovery process of community structure. Our algorithm can propagate the labels from the labeled nodes to the whole network nodes. The algorithm is evaluated on several artificial and real-world networks and shows that it is highly effective in recovering communities. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction. [ABSTRACT FROM AUTHOR]

Identifying critical nodes in complex networks has gained increasing attention in recent years. However, how to design an algorithm that has low computational complexity but can accurately identify important network nodes is still a challenge. Considering the role of structural holes in shaping communication channels, this paper presents an effective method based on local characteristics to identify critical nodes that play important roles in maintaining network connectivity. Our method considers the connections of a node as well as the connectivity of the neighborhood of the node. Through numerical simulations on various real-world networks, we have demonstrated that the proposed approach outperforms some other well-known heuristic algorithms in identifying vital nodes and leads to faster network collapse in target destruction. [ABSTRACT FROM AUTHOR]

With the development of economy and society, network analysis is widely used in more and more fields. Signed network has a good effect in the process of representation and display. As an important part of network analysis, fuzzy community detection plays an increasingly important role in analyzing and visualizing the real world. Fuzzy community detection helps to detect nodes that belong to some communities but are still closely related to other communities. These nodes are helpful for mining information from the network more realistically. However, there is little research in this field. This paper proposes a fuzzy community detection algorithm based on pointer and adjacency list. The model adopts a new ICALF network data structure, which can achieve the effect of storing community partition structure and membership value between community and node at the same time, with low time complexity and storage space. Experiments on real networks verify the correctness of the method, and prove that the method is suitable for large-scale network applications. [ABSTRACT FROM AUTHOR]

In this paper, we sketch and scrutinize the solitonic wave solution of Camassa–Holm equation by applying Kudryashov's new method. We promote the algorithm of our new method to find the new solutions of this essential model. Camassa–Holm equation is a recent model in the point of distortion of hierarchies composition of integrability systems. It has been displayed that these solutions have the shape of dark, bright and singular solitons solutions of Camassa–Holm nonlinear Schrodinger equation. Graphically changing of extracted results of this model (CH) has been separated to grasp the substantial evolution. We analyze the sensitivity of the obtained solutions on behalf of different boundary conditions. It is fair that our model furnishes an impressive mathematical mechanism for manufacturing the solutions of the traveling wave for many models in physics and mathematics. The strategy utilized here is straightforward and succinct. [ABSTRACT FROM AUTHOR]

Complex networks depict the individual relationship in a population, which can help to deeply mine the characteristics of complex networks and predict the potential collaboration between individuals by analyzing their interaction within different groups or clusters. However, the existing algorithms are with high complexity, which cost much computational time. In this paper, an efficient graph clustering algorithm based on spectral coarsening is proposed, to deal with the large time complexity of the traditional spectral algorithm. We first find the subset most possibly belonged to the same cluster in the original network, and merge them into a single node. The scale of the network will decrease with the network being coarsened. Then, the spectral clustering algorithm is performed on the coarsened network with the maintained advantages and the improved time efficiency. Finally, the experimental results on the multiple datasets demonstrate that the proposed algorithm, compared with the current state-of-the-art methods, has superior performance. [ABSTRACT FROM AUTHOR]

Community structure is an important and universal topological property of many complex networks such as social and information networks. The detection of communities of a network is a significant technique for understanding the structure and function of networks. In this paper, we propose an algorithm based on distributed learning automata for community detection (DLACD) in complex networks. In the proposed algorithm, each vertex of network is equipped with a learning automation. According to the cooperation among network of learning automata and updating action probabilities of each automaton, the algorithm interactively tries to identify high-density local communities. The performance of the proposed algorithm is investigated through a number of simulations on popular synthetic and real networks. Experimental results in comparison with popular community detection algorithms such as walk trap, Danon greedy optimization, Fuzzy community detection, Multi-resolution community detection and label propagation demonstrated the superiority of DLACD in terms of modularity, NMI, performance, min-max-cut and coverage. [ABSTRACT FROM AUTHOR]

Link community gradually unfolds its capacity in complex network research. In this paper, a novel link similarity measure on line graphs is proposed. This measure can be adapted to different types of networks with an adjustable parameter. We prove its value converges to a limit on line graphs with the relationship of the nonneighbor links taken into account. Based on this similarity measure, we propose a novel link community detection algorithm for link clustering on line graphs. The detection algorithm combines the novel link similarity measure with the classic Markov Cluster (MCL) Algorithm and determines the link community partitions by calculating an extended modularity measure. Extensive experiments on two types of complex networks demonstrate the effectiveness, reliability and rationality of our solution in contrast to the other two classical algorithms. [ABSTRACT FROM AUTHOR]

Local community detection algorithms are an important type of overlapping community detection methods. Local community detection methods identify local community structure through searching seeds and expansion process. In this paper, we propose a novel local community detection method on line graph through degree centrality and expansion (LCDDCE). We firstly employ line graph model to transfer edges into nodes of a new graph. Secondly, we evaluate edges relationship through a novel node similarity method on line graph. Thirdly, we introduce local community detection framework to identify local node community structure of line graph, combined with degree centrality and PageRank algorithm. Finally, we transfer them back into original graph. The experimental results on three classical benchmarks show that our LCDDCE method achieves a higher performance on normalized mutual information metric with other typical methods. [ABSTRACT FROM AUTHOR]

In order to solve the low efficiency of public opinion influence analysis of social media, a new public opinion influence algorithm K-adaboost has been proposed in this paper according to adaboost and K-means algorithms. We first group the training samples and calculate the clustering center of all types of users in the group using the K-means algorithm, and then train the weak classifier of public opinion data and confirm the influence of public opinion on all types of users using the adaboost algorithm, so as to get the total influence of public opinions. Finally, we compare and analyze the performance of K-adaboost, K-means and adaboost algorithms through simulation experiments. The results show that K-adaboost has good adaptability in convergence time and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, inspired by the pseudo-fractal networks (PFN) and the delayed pseudo-fractal networks (DPFN), we present a novel delayed pseudo-fractal networks model, denoted by NDPFN. Different from the generation algorithm of those two networks, every edge of the novel model has a time-delay to generate new nodes after producing one node. We derive exactly the main structural properties of the novel networks: degree distribution, clustering coefficient, diameter and average path length. Analytical results show that the novel networks have small-world effect and scale-free topology. Comparing topological parameters of these three networks, we find that the degree exponent of the novel networks is the largest while the clustering coefficient and the average path length are the smallest. It means that this kind of delay could weaken the heterogeneity and the small-world features of the network. Particularly, the delay effect in the NDPFN is contrary to that in the DPFN, which illustrates the variety of delay method could produce different effects on the network structure. These present findings may be helpful for a deeper understanding of the time-delay influence on the network topology. [ABSTRACT FROM AUTHOR]

Semisupervised community detection algorithms use prior knowledge to improve the performance of discovering the community structure of a complex network. However, getting those prior knowledge is quite expensive and time consuming in many real-world applications. This paper proposes an active semisupervised community detection algorithm based on the similarities between nodes. First, it transforms a given complex network into a weighted directed network based on the proposed asymmetric similarity method, some informative nodes are selected to be the labeled nodes by using an active mechanism. Second, the proposed algorithm discovers the community structure of a complex network by propagating the community labels of labeled nodes to their neighbors based on the similarity between a node and a community. Finally, the performance of the proposed algorithm is evaluated with three real networks and one synthetic network and the experimental results show that the proposed method has a better performance compared with some other community detection algorithms. [ABSTRACT FROM AUTHOR]

Timely and cost-effective analytics over social network has emerged as a key ingredient for success in many businesses and government endeavors. Community detection is an active research area of relevance to analyze online social network. The problem of selecting a particular community detection algorithm is crucial if the aim is to unveil the community structure of a network. The choice of a given methodology could affect the outcome of the experiments because different algorithms have different advantages and depend on tuning specific parameters. In this paper, we propose a community division model based on the notion of game theory, which can combine advantages of previous algorithms effectively to get a better community classification result. By making experiments on some standard dataset, it verifies that our community detection model based on game theory is valid and better. [ABSTRACT FROM AUTHOR]

Label propagation algorithm (LPA) attracts wide attention in community detection field for its near linear time complexity in large scale network. However, the algorithm adopts a random selection scheme in label updating strategy, which results in unstable division and poor accuracy. In this paper, five different indicators of node similarity are introduced based on network local information to distinguish nodes and a new label updating method is proposed. When there are multiple maximum neighbor labels in the propagation process, the maximum label corresponding to the most similar node is selected for updating instead of a random one. Five different forms of improved LPA are proposed which are named as SAL-LPA, SOR-LPA, JAC-LPA, SOR-LPA, HDI-LPA and HPI-LPA. The experiment results on real-world and artificial benchmark networks show that the improved LPA greatly improves the performance of the original algorithm, among which HPI-LPA is the best. [ABSTRACT FROM AUTHOR]

In this paper, based on Walktrap algorithm with the idea of random walk, and by selecting the neighbor communities, introducing improved signed probabilistic mixture (SPM) model and considering the edges within the community as positive links and the edges between the communities as negative links, a novel algorithm Walktrap-SPM for detecting overlapping community is proposed. This algorithm not only can identify the overlapping communities, but also can greatly increase the objectivity and accuracy of the results. In order to verify the accuracy, the performance of this algorithm is tested on several representative real-world networks and a set of computer-generated networks based on LFR benchmark. The experimental results indicate that this algorithm can identify the communities accurately, and it is more suitable for overlapping community detection. Compared with Walktrap, SPM and LMF algorithms, the presented algorithm can acquire higher values of modularity and NMI. Moreover, this new algorithm has faster running time than SPM and LMF algorithms. [ABSTRACT FROM AUTHOR]

The link prediction algorithm is one of the key technologies to reveal the inherent rule of network evolution. This paper proposes a novel link prediction algorithm based on the properties of the local community, which is composed of the common neighbor nodes of any two nodes in the network and the links between these nodes. By referring to the node degree and the condition of assortativity or disassortativity in a network, we comprehensively consider the effect of the shortest path and edge clustering coefficient within the local community on node similarity. We numerically show the proposed method provide good link prediction results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a link density clustering (LDC) method for overlapping community detection based on density peaks. We firstly use an extended cosine link distance metric to reflect the relationship of links. Then we introduce a clustering algorithm with fast search for solving the link clustering (LC) problem by density peaks with box plot strategy to determine the cluster centers automatically. Finally, we acquire both the link communities and the node communities. Our algorithm is compared with other representative algorithms through substantial experiments on real-world networks. The experimental results show that our algorithm consistently outperforms other algorithms in terms of modularity and coverage. [ABSTRACT FROM AUTHOR]

Community detection based on label propagation algorithm (LPA) has attracted widespread concern because of its high efficiency. But it is difficult to guarantee the accuracy of community detection as the label spreading is random in the algorithm. In response to the problem, an improved LPA based on random walk (RWLPA) is proposed in this paper. Firstly, a matrix measuring similarity among various nodes in the network is obtained through calculation. Secondly, during the process of label propagation, when a node has more than a neighbor label with the highest frequency, not the label of a random neighbor but the label of the neighbor with the highest similarity will be chosen to update. It can avoid label propagating randomly among communities. Finally, we test LPA and the improved LPA in benchmark networks and real-world networks. The results show that the quality of communities discovered by the improved algorithm is improved compared with the traditional algorithm. [ABSTRACT FROM AUTHOR]

The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb's dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application. [ABSTRACT FROM AUTHOR]