Detecting overlapping communities by seed community in weighted complex networks

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

Efficient algorithm based on neighborhood overlap for community identification in complex networks

Community structure is an important feature in many real-world networks. Many methods and algorithms for identifying communities have been proposed and have attracted great attention in recent years. In this paper, we present a new approach for discovering the community structure in networks. The novelty is that the algorithm uses the strength of the ties for sorting out nodes into communities. More specifically, we use the principle of weak ties hypothesis to determine to what community the node belongs. The advantages of this method are its simplicity, accuracy, and low computational cost. We demonstrate the effectiveness and efficiency of our algorithm both on real-world networks and on benchmark graphs. We also show that the distribution of link strength can give a general view of the basic structure information of graphs.     

Modelling of weighted evolving networks with community structures

Many social and biological networks consist of communities–groups of nodes within which links are dense but among which links are sparse. It turns out that most of these networks are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the link weights among their nodes. Recently, there are considerable interests in the study of properties as well as modelling of such networks with community structures. To our knowledge, however, no study of any weighted network model with such a community structure has been presented in the literature to date. In this paper, we propose a weighted evolving network model with a community structure. The new network model is based on the inner-community and inter-community preferential attachments and preferential strengthening mechanism. Simulation results indicate that this network model indeed reflect the intrinsic community structure, with various power-law distributions of the node degrees, link weights, and node strengths.     

Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have unordered discrete values, but many networks exhibit assortative mixing by some ordered (discrete or continuous) attribute, such as age or geographical location. In such cases, the identification of discrete communities may be difficult or impossible. We consider how the notion of community structure can be generalized to networks that have assortative mixing by ordered attributes. We propose a method of generating synthetic networks with ordered communities and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that current community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.     

The effect of weight on community structure of networks

The effect of weight on community structures is investigated in this paper. We use weighted modularity Q^w$Q^w$ to evaluate the partitions and weighted extremal optimization algorithm to detect communities. Starting from empirical and idealized weighted networks, the matching between weights and edges are disturbed. Then using similarity function S to measure the difference between community structures, it is found that the redistribution of weights does strongly affect the community structure especially in dense networks. This indicates that the community structure in networks is a suitable property to reflect the role of weight.     

Deterministic weighted scale-free small-world networks

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. We provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution, degree correlations, average clustering coefficient and degree-cluster correlations as well as the diameter.     

Recursive filtration method for detecting community structure in networks

Community detection is a topic of considerable recent interest within complex networks, but most methods proposed so far are divisive and agglomerative methods which delete only one edge each time to split the network, or agglomerating only one node each time until no individual node remains. Unlike those, we propose a method to split networks in parallel by deleting many edges in each filtration operation, and propose a community recursive coefficient (CRC) denoted by M instead of Q (modularity) to quantify the effect of the splitting results in this paper. We proved that recursive optimizing of the local M is equivalent to acquiring the maximal global Q value corresponding to good divisions. For a network with m edges, c communities and arbitrary topology, the method split the network at most c+1 times and detected the community structure in time O(m²+(c+1)m). We give several example applications, and show that the method can detect local communities according to the densities of external links to them in increasing order especially in large networks.     

A fast and efficient heuristic algorithm for detecting community structures in complex networks

Community structure is an important property of complex networks. How to detect the communities is significant for understanding the network structure and to analyze the network properties. Many algorithms, such as K-L and GN, have been proposed to detect community structures in complex networks. According to daily experience, a community should have many nodes and connections. Based on these principles and existing researches, a fast and efficient algorithm for detecting community structures in complex networks is proposed in this paper. The key strategy of the algorithm is to mine a node with the closest relations with the community and assign it to this community. Four real-world networks are used to test the performance of the algorithm. Experimental results demonstrate that the algorithm proposed is rather efficient for detecting community structures in complex networks.     

Detecting community structure in complex networks via node similarity

The detection of the community structure in networks is beneficial to understand the network structure and to analyze the network properties. Based on node similarity, a fast and efficient method for detecting community structure is proposed, which discovers the community structure by iteratively incorporating the community containing a node with the communities that contain the nodes with maximum similarity to this node to form a new community. The presented method has low computational complexity because of requiring only the local information of the network, and it does not need any prior knowledge about the communities and its detection results are robust on the selection of the initial node. Some real-world and computer-generated networks are used to evaluate the performance of the presented method. The simulation results demonstrate that this method is efficient to detect community structure in complex networks, and the ZLZ metrics used in the proposed method is the most suitable one among local indices in community detection.     

Evolving model of weighted networks inspired by scientific collaboration networks

Inspired by scientific collaboration networks (SCN), especially our empirical analysis of econophysicists network, an evolutionary model for weighted networks is proposed. Besides a new vertex added in at every time step, old vertices can also attempt to build up new links, or to reconnect the existing links. The number of connections repeated between two nodes is converted into the weight of the link. This provides a natural way for the evolution of link weight. The path-dependent preferential attachment mechanism with local information is also introduced. It increases the clustering coefficient of the network significantly. The model shows the scale-free phenomena in degree and vertex weight distribution. It also gives well qualitatively consistent behavior with the empirical results.     

Growing community networks with local events

The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes’ degrees.     

Synchronization in weighted complex networks: Heterogeneity and synchronizability

Synchronization in different types of weighted networks based on a scale-free weighted network model is investigated. It has been argued that heterogeneity suppresses synchronization in unweighted networks [T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91 (2003) 014101]. However, it is shown in this work that as the network becomes more heterogeneous, the synchronizability of Type I symmetrically weighted networks, and Type I and Type II asymmetrically weighted networks is enhanced, while the synchronizability of Type II symmetrically weighted networks is weakened.     

Semi-supervised clustering algorithm for community structure detection in complex networks

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.     

Epidemic spreading on weighted complex networks

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

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.     

Dynamical robustness analysis of weighted complex networks

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

Nonlinear growth in weighted networks with neighborhood preferential attachment

We propose a nonlinear growing model for weighted networks with two significant characteristics: (i) the new weights triggered by new edges at each time step grow nonlinearly with time; and (ii) a neighborhood local-world exists for local preferential attachment, which is defined as one selected node and its neighbors. Global strength-driven and local weight-driven preferential attachment mechanisms are involved in our model. We study the evolution process through both mathematical analysis and numerical simulation, and find that the model exhibits a wide-range power-law distribution for node degree, strength, and weight. In particular, a nonlinear degree–strength relationship is obtained. This nonlinearity implies that accelerating growth of new weights plays a nontrivial role compared with accelerating growth of edges. Because of the specific local-world model, a small-world property emerges, and a significant hierarchical organization, independent of the parameters, is observed.     

Quantum inspired evolutionary algorithm for community detection in complex networks

Community structure is indispensable to discover the potential property of complex network systems. In this paper we propose two algorithms (QIEA-net and iQIEA-net) to discover communities in social networks by optimizing modularity. Unlike many existing methods, the proposed algorithms adopt quantum inspired evolutionary algorithm (QIEA) to optimize a population of solutions and do not need to give the number of community beforehand, which is determined by optimizing the value of modularity function and needs no human intervention. In order to accelerate the convergence speed, in iQIEA-net, we apply the result of classical partitioning algorithm as a guiding quantum individual, which can instruct other quantum individuals' evolution. We demonstrate the potential of two algorithms on five real social networks. The results of comparison with other community detection algorithms prove our approaches have very competitive performance.