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It is a challenge in estimating the topology of a network from short time series data. In this paper, matching positions is developed to reconstruct the topology of a network from only one-step data. We consider a general network model of coupled agents, in which the phase transformation of each node is determined by its neighbors. From the phase transformation information from one step to the next, the connections of the tail vertices are reconstructed firstly by the matching positions. Removing the already reconstructed vertices, and repeatedly reconstructing the connections of tail vertices, the topology of the entire network is reconstructed. For sparse scale-free networks with more than ten thousands nodes, we almost obtain the actual topology using only the one-step data in simulations.

Network clustering phenomena are ubiquitous in nature and human society. In this paper, a method involving a network clustering model is proposed for mass segmentation in mammograms. First, the watershed transform is used to divide an image into regions, and features of the image are computed. Then a graph is constructed from the obtained regions and features. The network clustering model is applied to realize clustering of nodes in the graph. Compared with two classic methods, the algorithm based on the network clustering model performs more effectively in experiments.

Link prediction is a ubiquitous application in many fields which uses partially observed information to predict absence or presence of links between node pairs. The group evolving study provides reasonable explanations on the behaviors of nodes, relations between nodes and community formation in a network. Possible events in group evolution include continuing, growing, splitting, forming and so on. The changes discovered in networks are to some extent the result of these events. In this work, we present a group evolving-based characterization of node’s behavioral patterns, and via which we can estimate the probability they tend to interact. In general, the primary aim of this paper is to offer a minimal toy model to detect missing links based on evolution of groups and give a simpler explanation on the rationality of the model. We first introduce perturbations into networks to obtain stable cluster structures, and the stable clusters determine the stability of each node. Then fluctuations, another node behavior, are assumed by the participation of each node to its own belonging group. Finally, we demonstrate that such characteristics allow us to predict link existence and propose a model for link prediction which outperforms many classical methods with a decreasing computational time in large scales. Encouraging experimental results obtained on real networks show that our approach can effectively predict missing links in network, and even when nearly 40% of the edges are missing, it also retains stationary performance.

Inspired by the dynamics phenomenon occurred in social networks, the WJJLGS model is modified to imitate the clustering dynamics of signed social networks. Analyses show that the clustering dynamics of the model can be applied to partition signed social networks. Traditionally, blockmodel is applied to partition signed networks. In this paper, a detailed dynamics-based algorithm for signed social networks (DBAS) is presented. Simulations on several typical real-world and illustrative networks that have been analyzed by the blockmodel verify the correctness of the proposed algorithm. The efficiency of the algorithm is verified on large scale synthetic networks.

Community structure is ubiquitous in real world complex networks. Finding the communities is the key to understand the functions of those networks. A lot of works have been done in designing algorithms for community detection, but it remains a challenge in the field. Traditional modularity optimization suffers from the resolution limit problem. Recent researches show that combining the density based technique with the modularity optimization can overcome the resolution limit and an efficient algorithm named DenShrink was provided. The main procedure of DenShrink is repeatedly finding and merging micro-communities (broad sense) into super nodes until they cannot merge. Analyses in this paper show that if the procedure is replaced by finding and merging only dense pairs, both of the detection accuracy and runtime can be obviously improved. Thus an improved density-based algorithm: ImDS is provided. Since the time complexity, path based similarity indexes are difficult to be applied in community detection for high performance. In this paper, the path based Katz index is simplified and used in the ImDS algorithm.

The investigation of link prediction in networks is an important issue in many disciplines. The research of prediction algorithms which required short time but high accuracy is still a challenging task. Most of the existing algorithms are based on the topological information of the networks, including the local or global similarity indices. It is found that the hierarchical organization and community structure information may indeed provide insights for link prediction. In this paper, we propose a simple link prediction method, which fully explore the community structure information of the networks. Firstly, the community structure of the networks under different resolutions is extracted. Then, a simple frequency statistical model is applied to calculate how many times that a pair of nodes divided into the same community under different resolutions. Finally, the probability of the missing links is calculated. The performance of our algorithm is demonstrated by comparing with other seven well-known methods on two kinds of networks in different scales. The results indicate that our approach not only has a good performance on the accuracy, but also has a lower time complexity than any other algorithms which are based on hierarchical structure of the network.

The origin of evolutionary cooperation among individuals remains an unsolved issue across several disciplines; especially, the relation between the population structure and the emergence of cooperation is the key of the issue. Community structure is ubiquitous in social and biological networks. It is not clear until now whether the community structure promotes or inhibits cooperation. By defining the common neighbor coefficient of a network, the iteration dynamics of the prisoner’s dilemma game indicates that smaller value of the common neighbor coefficient of a network promotes cooperation in statistical significance for the prisoner’s dilemma game. Analyses show that the community networks usually have larger value of common neighbor coefficient than the ER random networks with the same number of nodes and edges, which shows that the community structure usually inhibits cooperation in the spatial prisoner’s dilemma game.

Community detection is one of the most important problems in complex networks. Many algorithms have been proposed in the last decade, and most of them focus on the non-overlapping community structures in the early days. Overlapping and hierarchical structures are another two important properties in complex networks, which have attracted researchers’ extensive concern in recent years. In this paper, we proposed a two-stage method which can detect the hierarchical, non-overlapping and overlapping community structures in complex networks. In this method, the CNM algorithm, a fast hierarchical agglomerative algorithm proposed by Clauset, Newman and Moore, is used in the first stage. In the second stage, a new evaluation function named as influence coefficient based on the local community structure is proposed, which can get the overlapping community structures at different overlapping levels by adjusting a tunable parameter. Besides, the proposed evaluation function can detect the wrongly classified nodes in the partition of the first stage and correct them. Finally, the computational complexity of the algorithm is low. The experimental results on both synthetic and real-world network datasets show the efficiency of our method.

A simple deterministic algorithm for community detection is provided by using two rounds of minimum spanning trees. By comparing the first round minimum spanning tree (1st-MST) with the second round spanning tree (2nd-MST) of the network, communities are detected and their overlapping nodes are also identified. To generate the two MSTs, a distance matrix is defined and computed from the adjacent matrix of the network. Compared with the resistance matrix or the communicability matrix used in community detection in the literature, the proposed distance matrix is very simple in computation. The proposed algorithm is tested on real world social networks, graphs which are failed by the modularity maximization, and the LFR benchmark graphs for community detection.

Motivated by social and biological interactions, a novel type of phase transition model is provided in order to investigate the emergence of the clustering phenomenon in networks. The model has two types of interactions: one is attractive and the other is repulsive. In each iteration, the phase of a node (or an agent) moves toward the average phase of its neighbors and moves away from the average phase of its non-neighbors. The velocities of the two types of phase transition are controlled by two parameters, respectively. It is found that the phase transition phenomenon is closely related to the topological structure of the underlying network, and thus can be applied to identify its communities and overlapping groups. By giving each node of the network a randomly generated initial phase and updating these phases by the phase transition model until they reach stability, one or two communities will be detected according to the nodes’ stable phases, confusable nodes are moved into a set named O f . By removing the detected communities and the nodes in O f , another one or two communities will be detected by an iteration of the algorithm, …. In this way, all communities and the overlapping nodes are detected. Simulations on both real-world networks and the LFR benchmark graphs have verified the efficiency of the proposed scheme.

In this paper, we propose a simple random network model with overlapping communities controlled by several parameters, and investigate the influence of the overlapping community structure on the synchronization behavior under different parameters. It is found that the synchronizability of the network is mainly influenced by the overlapping size of the communities and the connectivity density of the overlapped group to the other interrelated communities, and has nothing to do with the intra-connectivity of the overlapped group. In addition, it is found that the highly interconnected communities can be almost synchronized in a given time scale, whereas the overlapped group is far from synchronization. Furthermore, the instantaneous frequencies of the nodes in the communities and their overlapped group are also investigated, which show that the nodes in the overlapped group will exhibit a remarkable oscillation with a weighted mean frequency of the other correlative communities.

The Kuramoto model is modified by introducing a negative coupling strength, which is a generalization of the original one. Among the abundant dynamics, the clustering phenomenon of the modified Kuramoto model is analyzed in detail. After clustering appears in a network of coupled oscillators, the nodes are split into several clusters by their phases, in which the phases difference within each cluster is less than a threshold and larger than a threshold between different clusters. We show that this interesting phenomenon can be applied to identify the complete sub-graphs and further applied to graph coloring problems. Simulations on test beds of graph coloring problems have illustrated and verified the scheme.

Unidirectional coupled synchronization of two identical or different chaotic systems has been carefully studied based on the master–slave synchronization scheme, where the synchronous state is that of the master system and cannot be changed after they realized synchronization. In this paper, a general bidirectional synchronization scheme is presented which made the master–slave scheme a special case. It is straightforward to tune the synchronous state by just changing the value of a parameter. Based on the general bidirectional synchronization scheme, active control method is used to tune the synchronous state of two pairs of different chaotic systems: the Lorenz and Chen systems; and then the Lü and Rössler systems.

The investigation of community structures is one of the most important problems in the field of complex networks and has countless applications in different disciplines: biology, computer, social sciences, etc. Many community detection algorithms have been developed in various fields recently. The vast majority of these algorithms only find disjoint communities; however, in many real-world networks communities often overlap to some extent. In this paper, we propose an efficient method for adjusting these classical algorithms to match the requirement for discovering overlapping communities in complex networks, which is based on a local definition of community strength. The method can in principle be applied with any clustering algorithm. Tests on a set of computer generated and real-world networks give excellent results. In particular, we show that the method can also allow one to availably analyze the problem of unstable nodes in community detection, which is very helpful for understanding the structural properties of the networks correctly and comprehensively.

Based on the work of Nishikawa and Motter, who have extended the well-known master stability framework to include non-diagonalizable cases, we develop another extension of the master stability framework to obtain criteria for global synchronization. Several criteria for global synchronization are provided which generalize some previous results. The Jordan canonical transformation method is used in stead of the matrix diagonalization method. Especially, we show clearly that, the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second-largest eigenvalue, even though all the eigenvalues of the nonsymmetric coupling matrix are real. Furthermore, the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed. Numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two-cell cellular neural network.

Based on a general complex dynamic network model with nonsymmetrical time-delay coupling, and without assuming irreducibility, a strategy for global exponential synchronization is proposed based on the approach of linear state feedback controllers. Especially, the criteria for controller design can be expressed by inequalities instead of matrix inequalities; thus the proposed controllers can be easily constructed without relying on any numerical toolbox. The efficiency of the control scheme is revealed by simulations on a network consisting of the unified chaotic systems with nearest-neighbour unidirectional time-delay coupling.

A new general complex delayed dynamical network model with nonsymmetric coupling is introduced, and then we investigate its synchronization phenomena. Several synchronization criteria for delay-independent and delay-dependent synchronization are provided which generalize some previous results. The matrix Jordan canonical formalization method is used instead of the matrix diagonalization method, so in our synchronization criteria, the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues. Especially, we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second-largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real. Furthermore, the effects of time-delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures. The results are illustrated by delayed networks in which each node is a two-dimensional limit cycle oscillator system consisting of a two-cell cellular neural network, numerical simulations show that these networks can realize synchronization with smaller time-delay, and will lose synchronization when the time-delay increase larger than a threshold.

Based on a general complex dynamical network model with nonsymmetric coupling, some criteria for synchronization are proposed based on the approach of state observer design. Unlike the nonobserver-based dynamical networks, where the coupling between two connected nodes is defined by an inner coupling matrix and full state coupling is typically needed, in this paper, smaller amount of coupling variables or even only a scalar output signal of each node is needed to synchronize the network. Unlike the commonly researched complex network model, where the coupling between nodes is symmetric, here, in our network model, the coupling configuration matrix is not assumed to be symmetric and may have complex eigenvalues. The matrix Jordan canonical formalization method is used instead of the matrix diagonalization method, so in our synchronization criteria, the coupling configuration matrix is not required to be diagonalizable. Especially, the proposed step-by-step approach is simpler in computation than the existent ones, which usually rely heavily on numerical toolbox, and may be done by hand completely. An example is given to illustrate the step-by-step approach, in which each node is a two-dimensional dynamical limit cycle oscillator system consisting of a two-cell cellular neural network, and numerical simulations are also done to verify the results of design.