LPA-MNI: An Improved Label Propagation Algorithm Based on Modularity and Node Importance for Community Detection

Community detection is of great significance in understanding the structure of the network. Label propagation algorithm (LPA) is a classical and effective method, but it has the problems of randomness and instability. An improved label propagation algorithm named LPA-MNI is proposed in this study by combining the modularity function and node importance with the original LPA. LPA-MNI first identify the initial communities according to the value of modularity. Subsequently, the label propagation is used to cluster the remaining nodes that have not been assigned to initial communities. Meanwhile, node importance is used to improve the node order of label updating and the mechanism of label selecting when multiple labels are contained by the maximum number of nodes. Extensive experiments are performed on twelve real-world networks and eight groups of synthetic networks, and the results show that LPA-MNI has better accuracy, higher modularity, and more reasonable community numbers when compared with other six algorithms. In addition, LPA-MNI is shown to be more robust than the traditional LPA algorithm.     

Detecting community structure using label propagation with weighted coherent neighborhood propinquity

Community detection has become an important methodology to understand the organization and function of various real-world networks. The label propagation algorithm (LPA) is an almost linear time algorithm proved to be effective in finding a good community structure. However, LPA has a limitation caused by its one-hop horizon. Specifically, each node in LPA adopts the label shared by most of its one-hop neighbors; much network topology information is lost in this process, which we believe is one of the main reasons for its instability and poor performance. Therefore in this paper we introduce a measure named weighted coherent neighborhood propinquity (weighted-CNP) to represent the probability that a pair of vertices are involved in the same community. In label update, a node adopts the label that has the maximum weighted-CNP instead of the one that is shared by most of its neighbors. We propose a dynamic and adaptive weighted-CNP called entropic-CNP by using the principal of entropy to modulate the weights. Furthermore, we propose a framework to integrate the weighted-CNP in other algorithms in detecting community structure. We test our algorithm on both computer-generated networks and real-world networks. The experimental results show that our algorithm is more robust and effective than LPA in large-scale networks.     

Growth curve based label propagation algorithm for community detection

How to better and faster identify the community structure is a hot issue in complex networks. During the past decades, various attempts have been made to solve this issue. Amongst them, without doubt, label propagation algorithm (LPA) is one of the most satisfying answers, especially for large-scale networks. However, it has one major flaw that when the community structure is not clear enough, a monster community tends to form. To address this issue, we set a growth curve for communities, gradually increasing from a low capacity to a higher capacity over time. Further, we improve the mechanism of label choosing for small communities to escape from local maximum. The experimental results on both synthetic and real networks demonstrate that our algorithm not only enhances the detection ability of the traditional label propagation algorithm, but also improves the quality of the identified communities.     

Detecting community structure using label propagation with consensus weight in complex network

Community detection is a fundamental work to analyse the structural and functional properties of complex networks.The label propagation algorithm(LPA) is a near linear time algorithm to find a good community structure. Despite various ubsequent advances, an important issue of this algorithm has not yet been properly addressed. Random update orders within the algorithm severely hamper the stability of the identified community structure. In this paper, we executed the asic label propagation algorithm on networks multiple times, to obtain a set of consensus partitions. Based on these onsensus partitions, we created a consensus weighted graph. In this consensus weighted graph, the weight value of the dge was the proportion value that the number of node pairs allocated in the same cluster was divided by the total number f partitions. Then, we introduced consensus weight to indicate the direction of label propagation. In label update steps,y computing the mixing value of consensus weight and label frequency, a node adopted the label which has the maximum mixing value instead of the most frequent one. For extending to different networks, we introduced a proportion parameter o adjust the proportion of consensus weight and label frequency in computing mixing value. Finally, we proposed an pproach named the label propagation algorithm with consensus weight(LPAcw), and the experimental results showed that he LPAcw could enhance considerably both the stability and the accuracy of community partitions.     

Directed LPA: Propagating labels in directed networks

Ignoring edge directionality and considering the graph as undirected is a common approach to detect communities in directed networks. However, it's not a meaningful way due to the loss of information captured by the edge property. Even if Leicht and Newman extended the original modularity to a directed version to address this issue, the problem of distinguishing the directionality of the edges still exists in maximizing modularity algorithms. To this direction, we extend one of the most famous scalable algorithms, namely label propagation algorithm (LPA), to a directed case, which can recognize the flow direction among nodes. To explore what properties the directed modularity should have, we also use another directed modularity, called LinkRank, and provide an empirical study. The experimental results on both real and synthetic networks demonstrate that the proposed directed algorithms can not only make use of the edge directionality but also keep the same time complexity as LPA.     

Community detection in social networks based on improved Label Propagation Algorithm and balanced link density

Nowadays, community detection has been raised as one of the key research areas in the online social networks mining. One of the most common algorithms in this field is label propagation algorithm (LPA). Even though the LPA method has advantages such as simplicity in understanding and implementation, as well as linear time complexity, it has an important disadvantage of the uncertainty and instability in outcomes, that is, the algorithm detects and reports different combinations of communities in each run. This problem originates from the nature of random selection in the LPA method. In this paper, a novel method is proposed based on the LPA method and the inherent structure, that is, link density feature, of the input network. The proposed method uses a sensitivity parameter (balance parameter); by choosing the appropriate values for it, the desired qualities of the identified communities can be achieved. The proposed method is called Balanced Link Density-based Label Propagation (BLDLP). In comparison with the basic LPA, the proposed method has an advantage of certainty and stability in the output results, whereas its time complexity is still comparable with the basic LPA and of course lowers than many other approaches. The proposed method has been evaluated on real-world known datasets, such as the Facebook social network and American football clubs, and by comparing it with the basic LPA, the effectiveness of the proposed method in terms of the quality of the communities found and the time complexity has been shown.     

Robust network community detection using balanced propagation

Label propagation has proven to be an extremely fast method for detecting communities in large complex networks. Furthermore, due to its simplicity, it is also currently one of the most commonly adopted algorithms in the literature. Despite various subsequent advances, an important issue of the algorithm has not yet been properly addressed. Random (node) update orders within the algorithm severely hamper its robustness, and consequently also the stability of the identified community structure. We note that an update order can be seen as increasing propagation preferences from certain nodes, and propose a balanced propagation that counteracts for the introduced randomness by utilizing node balancers. We have evaluated the proposed approach on synthetic networks with planted partition, and on several real-world networks with community structure. The results confirm that balanced propagation is significantly more robust than label propagation, when the performance of community detection is even improved. Thus, balanced propagation retains high scalability and algorithmic simplicity of label propagation, but improves on its stability and performance.     

Advanced modularity-specialized label propagation algorithm for detecting communities in networks

A modularity-specialized label propagation algorithm (LPAm) for detecting network communities was recently proposed. This promising algorithm offers some desirable qualities. However, LPAm favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space. To escape local maxima, we employ a multistep greedy agglomerative algorithm (MSG) that can merge multiple pairs of communities at a time. Combining LPAm and MSG, we propose an advanced modularity-specialized label propagation algorithm (LPAm+). Experiments show that LPAm+ successfully detects communities with higher modularity values than ever reported in two commonly used real-world networks. Moreover, LPAm+ offers a fair compromise between accuracy and speed.     

Overlapping Community Detection Based on Membership Degree Propagation

A community in a complex network refers to a group of nodes that are densely connected internally but with only sparse connections to the outside. Overlapping community structures are ubiquitous in real-world networks, where each node belongs to at least one community. Therefore, overlapping community detection is an important topic in complex network research. This paper proposes an overlapping community detection algorithm based on membership degree propagation that is driven by both global and local information of the node community. In the method, we introduce a concept of membership degree, which not only stores the label information, but also the degrees of the node belonging to the labels. Then the conventional label propagation process could be extended to membership degree propagation, with the results mapped directly to the overlapping community division. Therefore, it obtains the partition result and overlapping node identification simultaneously and greatly reduces the computational time. The proposed algorithm was applied to a synthetic Lancichinetti–Fortunato–Radicchi (LFR) dataset and nine real-world datasets and compared with other up-to-date algorithms. The experimental results show that our proposed algorithm is effective and outperforms the comparison methods on most datasets. Our proposed method significantly improved the accuracy and speed of the overlapping node prediction. It can also substantially alleviate the computational complexity of community structure detection in general.     

有限步传播范围期望指标判别节点传播影响力

在线社交网络逐渐成为人们不可或缺的重要工具,识别网络中具有高影响力的节点作为初始传播源,在社会感知与谣言控制等方面具有重要意义.本文基于独立级联模型,给出了一个描述有限步传播范围期望的指标-传播度,并设计了一种高效的递推算法.该指标在局部拓扑结构信息的基础上融合了传播概率对影响力进行刻画,能够较好地反映单个节点的传播影响力.对于多传播源影响力极大化问题,本文提出了一种基于传播度的启发式算法-传播度折扣算法,使得多个传播源的联合影响力最大.最后,将上述方法应用到三个真实网络中,与经典指标和方法相比,该方法不需要知道网络的全局结构信息,而是充分了利用网络的局部结构信息,可以较快地筛选出高传播影响力的传播源.     

Image segmentation using adaptive loopy belief propagation

Loopy belief propagation (LBP) algorithm over pairwise-connected Markov random fields (MRFs) has become widely used for low-level vision problems. However, Pairwise MRF is often insufficient to capture the statistics of natural images well, and LBP is still extremely slow for application on an MRF with large discrete label space. To solve these problems, the present study proposes a new segmentation algorithm based on adaptive LBP. The proposed algorithm utilizes local region information to construct a local region model, as well as a local interaction region MRF model for image segmentation. The adaptive LBP algorithm maximizes the global probability of the proposed MRF model, which employs two very important strategies, namely, “message self-convergence” and “adaptive label pruning”. Message self-convergence can improve the reliability of a pixel in choosing a label in local region, and label pruning can dismiss impossible labels for every pixel. Thus, the most reliable information messages transfer through the LBP algorithm. The experimental results show that the proposed algorithm not only obtains more accurate segmentation results but also greater speed.     

Attractive target wave patterns in complex networks consisting of excitable nodes

This review describes the investigations of oscillatory complex networks consisting of excitable nodes,focusing on the target wave patterns or say the target wave attractors.A method of dominant phase advanced driving(DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations,such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks.The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns.Therefore,the center(say node A) and its driver(say node B) of a target wave can be used as a label,(A,B),of the given target pattern.The label can give a clue to conveniently retrieve,suppress,and control the target waves.Statistical investigations,both theoretically from the label analysis and numerically from direct simulations of network dynamics,show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large,and all these attractors can be labeled and easily controlled based on the information given by the labels.The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.     

Characteristics of an envelope model for laser–plasma accelerator simulation

Simulation of laser–plasma accelerator (LPA) experiments is computationally intensive due to the disparate length scales involved. Current experiments extend hundreds of laser wavelengths transversely and many thousands in the propagation direction, making explicit PIC simulations enormously expensive and requiring massively parallel execution in 3D. Simulating the next generation of LPA experiments is expected to increase the computational requirements yet further, by a factor of 1000. We can substantially improve the performance of LPA simulations by modeling the envelope evolution of the laser field rather than the field itself. This allows for much coarser grids, since we need only resolve the plasma wavelength and not the laser wavelength, and therefore larger timesteps can be used. Thus an envelope model can result in savings of several orders of magnitude in computational resources. By propagating the laser envelope in a Galilean frame moving at the speed of light, dispersive errors can be avoided and simulations over long distances become possible. The primary limitation to this envelope model is when the laser pulse develops large frequency shifts, and thus the slowly-varying envelope assumption is no longer valid. Here we describe the model and its implementation, and show rigorous benchmarks for the algorithm, establishing second-order convergence and correct laser group velocity. We also demonstrate simulations of LPA phenomena such as self-focusing and meter-scale acceleration stages using the model.     

节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.     

A brief study on coevolution of Ising dynamics

Community structure appears to be an intrinsic property of many complex real-world networks. However, recent work shows that real-world networks reveal even more sophisticated modules than classical cohesive (link-density) communities. In particular, networks can also be naturally partitioned according to similar patterns of connectedness among the nodes, revealing link-pattern communities. We here propose a propagation based algorithm that can extract both link-density and link-pattern communities, without any prior knowledge of the true structure. The algorithm was first validated on different classes of synthetic benchmark networks with community structure, and also on random networks. We have further applied the algorithm to different social, information, technological and biological networks, where it indeed reveals meaningful (composites of) link-density and link-pattern communities. The results thus seem to imply that, similarly as link-density counterparts, link-pattern communities appear ubiquitous in nature and design.     

Optimal selection of nodes to propagate influence on networks

How to optimize the spreading process on networks has been a hot issue in complex networks, marketing, epidemiology, finance, etc. In this paper, we investigate a problem of optimizing locally the spreading: identifying a fixed number of nodes as seeds which would maximize the propagation of influence to their direct neighbors. All the nodes except the selected seeds are assumed not to spread their influence to their neighbors. This problem can be mapped onto a spin glass model with a fixed magnetization. We provide a message-passing algorithm based on replica symmetrical mean-field theory in statistical physics, which can find the nearly optimal set of seeds. Extensive numerical results on computer-generated random networks and real-world networks demonstrate that this algorithm has a better performance than several other optimization algorithms.     

基于自规避随机游走的节点排序算法

评估复杂网络系统的节点重要性有助于提升其系统抗毁性和结构稳定性. 目前, 定量节点重要性的排序算法通常基于网络结构的中心性指标如度数、介数、紧密度、特征向量等. 然而, 这些算法需要以知晓网络结构的全局信息为前提, 很难在大规模网络中实际应用. 基于自规避随机游走的思想, 提出一种结合网络结构局域信息和标签扩散的节点排序算法. 该算法综合考虑了节点的直接邻居数量及与其他节点之间的拓扑关系, 能够表征其在复杂网络系统中的结构影响力和重要性. 基于三个典型的实际网络, 通过对极大连通系数、网络谱距离数、节点连边数和脆弱系数等评估指标的实验对比, 结果表明提出的算法显著优于现有的依据局域信息的节点排序算法.     

OCDMA Network and Key Technology

OCDMA's network application on LAN, metro-ring and backbone networks are discussed. Its simple tell-go protocol makes it a powerful competitor with CSMA/CD in optical LANs. Its large soft capacity could erase the wavelength routing algorithm of WDM based metro-ring. And its content susceptibility could be largely used in label switching backbone network. And why should be 2D CODEC as well as interference cancellation is although mentioned as OCDMA key technology.     

Astrocyte signaling in the presence of spatial inhomogeneities

Astrocytes, a special type of glial cells, were considered to have just a supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by various neurotransmitters, such as ATP, and can generate Ca2+ and ATP waves, which can propagate over many cell lengths before being blocked. Although pathological conditions, such as spreading depression and epilepsy, have been linked to abnormal wave propagation in astrocytic cellular networks, a quantitative understanding of the underlying characteristics is still lacking. Astrocytic cellular networks are inhomogeneous, in the sense that the domain they occupy contains passive regions or gaps, which are unable to support wave propagation. Thus, this work focuses on understanding the complex interplay between single-cell signal transduction, domain inhomogeneity, and the characteristics of wave propagation and blocking in astrocytic cellular networks. The single-cell signal transduction model that was employed accounts for ATP-mediated IP3 production, the subsequent Ca2+ release from the ER, and ATP release into the extracellular space. The model is excitable and thus an infinite range of wave propagation is observed if the domain of propagation is homogeneous. This is not always the case for inhomogeneous domains. To model wave propagation in inhomogeneous astrocytic networks, a reaction-diffusion framework was developed and one-gap as well as multiple-gap cases were simulated using an efficient finite-element algorithm. The minimum gap length that blocks the wave was computed as a function of excitability levels and geometric characteristics of the inhomogeneous network, such as the length of the active regions (cells). Complex transient patterns, such as wave reflection, wave trapping, and generation of echo waves, were also predicted by the model, and their relationship to the geometric characteristics of the network was evaluated. Therefore, the proposed model can help in the formulation of testable hypotheses to explain the observed abnormal wave propagation in pathological situations.     

Inference and phase transitions in the detection of modules in sparse networks

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks generated by stochastic block models. Using the cavity method of statistical physics and its relationship to belief propagation, we unveil a phase transition from a regime where we can infer the correct group assignments of the nodes to one where these groups are undetectable. Our approach yields an optimal inference algorithm for detecting modules, including both assortative and disassortative functional modules, assessing their significance, and learning the parameters of the underlying block model. Our algorithm is scalable and applicable to real-world networks, as long as they are well described by the block model.