Generalized Louvain method for community detection in large networks

Community detection in complex networks remains a fundamental problem in network science, with wideranging applications from sociology to biology and recommendation systems.Building on recent advances in label diffusion techniques, we propose a novel hybrid approach-GraphSAGE-LBLD-that combines the structural awareness of the GraphSAGE embedding model with the local balance and speed advantages of the Label Balanced Label Diffusion (LBLD) algorithm.Our method integrates representation learning into the label propagation process, allowing for more semantically meaningful diffusion and improved stability across diverse network topologies.We empirically evaluate GraphSAGE-LBLD on multiple real-world SNAP datasets and benchmark against Louvain, classic Label Propagation, and the original LBLD.Results demonstrate that our model consistently achieves higher modularity and Normalized Mutual Information (NMI) scores, while maintaining comparable runtime.The integration of GraphSAGE enhances the representation of local neighbourhoods, resulting in finer community boundaries and better detection of small or overlapping clusters.Our method offers a practical, scalable, and more accurate alternative for modern community detection tasks.

A New Randomized Algorithm for Community Detection in Large Networks

It is common in the study of networks to investigate intermediate-sized (or "meso-scale") features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are typically construed as sets of nodes with denser connections internally than with the remainder of a network. In this paper, we adopt a complementary perspective that communities are associated with bottlenecks of locally biased dynamical processes that begin at seed sets of nodes, and we employ several different community-identification procedures (using diffusion-based and geodesic-based dynamics) to investigate community quality as a function of community size. Using several empirical and synthetic networks, we identify several distinct scenarios for "size-resolved community structure" that can arise in real (and realistic) networks: (1) the best small groups of nodes can be better than the best large groups (for a given formulation of the idea of a good community); (2) the best small groups can have a quality that is comparable to the best medium-sized and large groups; and (3) the best small groups of nodes can be worse than the best large groups. As we discuss in detail, which of these three cases holds for a given network can make an enormous difference when investigating and making claims about network community structure, and it is important to take this into account to obtain reliable downstream conclusions. Depending on which scenario holds, one may or may not be able to successfully identify "good" communities in a given network (and good communities might not even exist for a given community quality measure), the manner in which different small communities fit together to form meso-scale network structures can be very different, and processes such as viral propagation and information diffusion can exhibit very different dynamics. In addition, our results suggest that, for many large realistic networks, the output of locally biased methods that focus on communities that are centered around a given seed node (or set of seed nodes) might have better conceptual grounding and greater practical utility than the output of global community-detection methods. They also illustrate structural properties that are important to consider in the development of better benchmark networks to test methods for community detection.

VLSI designs contain very large resistive networks consisting of hundreds of millions (10e11) of resistors. Accurate parasitic extraction and analysis of such large networks is essential in many phases of the VLSI design flow. Existing techniques to analyze large resistive networks using linear solvers, despite recent optimizations, still take prohibitive computation time. In this paper a new technique based on low-distortion embedding to estimate point-to-point effective resistance is presented. Our proposed method employs recently discovered techniques from theoretical computer science to compute an e-approximate resistance embedding matrix from which effective resistances of all node pairs can be estimated as easily as taking the Euclidean norm of column differences. The proposed method runs in almost linear time (linear in the number of resistors), and the accuracy (e) is user specified. The method has been implemented and experimental results on large networks containing upto 10e11 nodes are presented. Compared to existing method using sparse linear solvers, our methods are more than 10 times faster on mesh networks and more importantly given a network of n nodes, allow computation of effective resistance between arbitrary node pairs in O(lg(n)) time (lg denotes logarithm to base 2).

In this paper, three new algorithms, a greedy algorithm, a KL-like algorithm, and an add-all algorithm, are proposed to find local optimal community structures in large networks starting from a given source vertex. The time complexity for finding a local community of all these algorithms is O(K 2d), where K is the number of vertices to be explored in the sub-graph and d is the average degree of the vertices in the sub-graph. A JAVA tool is developed based on these algorithms to identify local community structures in large networks. The results of using this tool to analyze a co-purchase network from Amazon.com show that local community structures exist in this large-scale co-purchase network. Further analyses of the identified local communities show that purchases of media items form more compact local communities than purchases of book items do, indicating that recommending digital media items to customers based on co-purchasing information in the online store is more efficient than recommending books.

Centrality measures for networks with community structure

Community detection in complex networks is an important multidisciplinary research area and is considered crucial for understanding the structure of complex networks. Unsupervised deep learning models (e.g. stack autoencoders) have been successfully proposed for the problem of community detection, which can extract network features and use them in splitting the network into communities. Despite their effectiveness, these methods are not very efficient, especially when large networks are involved. Furthermore, existing models usually handle the network as a single object, which means that massive trainable parameters are required during training (which in normal complex networks often reach millions of parameters, not to mention large networks), thereby increasing the complexity of the model. To overcome these problems, this paper proposes a deep autoencoder method for network community detection based on three techniques: network-data partitioning, reduction and sharing of trainable parameters, which contribute significantly to improve the efficiency of the method. A new partitioning strategy is imposed on complex networks at different levels. The paper also proposes a parallel design for the proposed method. Furthermore, a new similarity constraint function is proposed to improve and preserve the performance of community detection task. We performed extensive experiments for different partitioning levels of a network-dataset to evaluate the method with CPU and GPU devices. The results showed that the proposed method significantly improved training speed and efficiency while maintaining performance. The results also showed that the efficiency of the method increases as we move to a deeper level of partitioning.

Some biologists have abandoned the idea that computational efficiency in processing multipart tasks or input sets alone drives the evolution of modularity in biological networks. A recent study confirmed that small modular (neural) networks are relatively computationally-inefficient but large modular networks are slightly more efficient than non-modular ones. The present study determines whether these efficiency advantages with network size can drive the evolution of modularity in networks whose connective architecture can evolve. The answer is no, but the reason why is interesting. All simulations (run in a wide variety of parameter states) involving gradualistic connective evolution end in non-modular local attractors. Thus while a high performance modular attractor exists, such regions cannot be reached by gradualistic evolution. Non-gradualistic evolutionary simulations in which multi-modularity is obtained through duplication of existing architecture appear viable. Fundamentally, this study indicates that computational efficiency alone does not drive the evolution of modularity, even in large biological networks, but it may still be a viable mechanism when networks evolve by non-gradualistic means.

Complex networks have in generally communities. These communities are very important. Network’s communities represent sets of nodes, which are very connected. In this research, we developed a new method to find the community structure in networks. Our method is based on flower pollination algorithm (FPA) witch is used in the splitting process. The splitting of networks in our method maximizes a function of quality called modularity. We provide a general framework for implementing our new method to find community structure in networks. We present the effectiveness of our method by comparison with some known methods on computer-generated and real-world networks.

CoVeC: Coarse-grained vertex clustering for efficient community detection in sparse complex networks

Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new measure based on stochastic diffusion processes, the transmission centrality, that captures the importance of links by estimating the average number of nodes to whom they transfer information during a global spreading diffusion process. We propose a simple algorithmic solution to compute transmission centrality and to approximate it in very large networks at low computational cost. Finally we apply transmission centrality in the identification of weak ties in three large empirical social networks, showing that this metric outperforms other centrality measures in identifying links that drive spreading processes in a social network.

Principles of Wireless Cloud Coding The termWireless Cloud Coding (WCC) will denote the coding concept suited for large and complex networks with a stochastic structure and connectivity. A simple low-scale WPNC network with a known deterministic structure can be designed in a “handcrafted” style.We usually also easily identify the critical points of performance or design aspects that need to be optimized. On the other hand, a complex large stochastic network adds some specific problems. Stochastic Network Structure The network structure and connectivity may be stochastic and unknown. A standard NCM design needs to know the participating signals forming the H-constellation in the H-MAC stage, and also the full end-to-end hierarchical encapsulation of all involved HNC maps to guarantee the end-to-end solvability. In a large randomly changing network, this creates a significant problem for (a) identifying and estimating the system/ channel state, (b) making a decision on the processing form , and (c) signaling this decision to all involved nodes. Instead of using this traditional solution, we can try to devise the NCM that is blind to the network structure that will not require a separate NCM/WPNC control protocol but will treat the unknown network structure as an additional degree of freedom fully integrated with the actual payload data (see Section 10.2). Clustered, Nested, and Modular Cloud Framework The number of the design degrees of freedom may be prohibiting in a large network. A nested modular encapsulation of some of its fragments/clusters can help. This has two aspects. (a) It simplifies the overall design by clustering the nodes and nesting the clusters. (b) Each cluster performs some processing as a “black-box” self-contained virtual super-node . It does not reveal its internal structure to the outside world and simply provides some functionality as a super-node. Its global level of clustering can even comprise the whole cloud. It can serve its outside terminals as if it was some super-relay performing some complex internal hidden processing (see Section 10.3). Wireless Cloud-Coding-Based Design of NCM Random Channel Class H-MAC and Joint HNC Map Joint HNC map vs. Classical Signaling A classical signaling solution (Figure 10.1a) is based on the channel sensing and then switching the NCM map at the node depending on the channel class (connection/ disconnection).

Measuring the centrality of nodes in real-world networks has remained an important task in the technological, social, and biological network paradigms carrying implications on their analysis and applications. Exact inference of centrality values is infeasible in large networks due to the need to solve the all-pairs shortest path problem. We introduce a framework to approximate node centralities in real-world networks that are known to exhibit modularity, i.e., the presence of dense subgraphs or communities, which are themselves sparsely connected. We also propose a novel centrality measure known as Community Inbetweenness that ranks nodes based solely on community information. In a modular network of size n with √n(1/2) evenly sized communities and m edges, our framework requires linear time O(m) and O(√nm) time for the approximation of closeness and betweenness respectively. Utilizing a recently proposed linear time method in community detection, our approximation techniques are faster than traditional sampling algorithms, applicable in real-time distributed environments, and offer highly comparable results.

In the process of research on the characteristic detection method for large scale network attacks, due to the use of the current algorithm for large-scale network attack detection, it is unable to describe the attack characteristics of network attacks or detect in low accuracy. Therefore, an attack detection method for large scale network based on cooperative planning is proposed. The method is based on collaborative planning to design the detection characteristic of large scale network attacks, which is transformed into a space search problem. The difference between the parameters of the flow vector and the normal vector of the normal network spatial data is extracted as characteristics, combining Gauss mixture model with the expectation maximization algorithm, to design Lorenz chaotic asynchronous tracking detection algorithm for modeling and detection of network data stream. The experimental simulation shows that the detection method of large scale network attack detection method has high accuracy and high efficiency. Currently, characteristic detection technology for network attack is based on ant colony algorithm, particle algorithm and the fuzzy algorithm for large-scale network. Among them, the commonly characteristic detection method is technology based on the fuzzy algorithm for large scale network attack. However the current algorithms with characteristic detection for network attack could not describe attack characteristics in detail, which lead to low accuracy. In view of the above defect, a method for large scale network attack detection based on cooperative planning is proposed. The method is represented for network attack with characteristic feature, which is transformed into a search problem in the space. To extract difference of parameter vector characteristic of network spatial data flow between to test network and normal network, with Gaussian mixture model and expectation maximization algorithm combined, Lorenz chaotic asynchronous detecting and tracking algorithm is designed to model and test the network data flow. The experimental simulation shows that the detection method for large scale network has high accuracy and efficiency.

Communication has become a lot easier with the advent of easy and cheap means of reaching people across the globe. This has allowed the development of large networked communities and, with the technology available to track them, has opened up the study of social networks at unprecedented scales. This has necessitated the scaling up of various network analysis algorithms that have been proposed earlier in the literature. While some algorithms can be readily adapted to large networks, in many cases the adaptation is not trivial. In this work, we explore the scaling up of a class of node centrality algorithms based on cooperative game theory. These were proposed earlier as an efficient alternatives to traditional measure of information diffusion centrality. We present here distributed versions of these algorithms in a Map-Reduce framework, currently the most popular distributed computing paradigm. We empirically demonstrate the scaling behavior of our algorithm on very large synthetic networks thereby establishing the utility of these methods in settings such as online social networks.