Benchmark model to assess community structure in evolving networks

Detecting the time evolution of the community structure of networks is crucial to identify major changes in the internal organization of many complex systems, which may undergo important endogenous or exogenous events. This analysis can be done in two ways: considering each snapshot as an independent community detection problem or taking into account the whole evolution of the network. In the first case, one can apply static methods on the temporal snapshots, which correspond to configurations of the system in short time windows, and match afterwards the communities across layers. Alternatively, one can develop dedicated dynamic procedures, so that multiple snapshots are simultaneously taken into account while detecting communities, which allows us to keep memory of the flow. To check how well a method of any kind could capture the evolution of communities, suitable benchmarks are needed. Here we propose a model for generating simple dynamic benchmark graphs, based on stochastic block models. In them, the time evolution consists of a periodic oscillation of the system's structure between configurations with built-in community structure. We also propose the extension of quality comparison indices to the dynamic scenario.Comment: 11 pages, 7 figures, 3 table

A parallel self-organizing community detection algorithm based on swarm intelligence for large scale complex networks

Community detection is a critical task for complex network analysis. It helps us to understand the properties of the system that a complex network represents and has significance to a wide range of applications. Nowadays, the challenges faced by community detection algorithms include overlapping community structure detection, large scale network analysis, dynamic changing of analyzed network topology and many more. In this paper a self-organizing community detection algorithm, based on the idea of swarm intelligence, was proposed and its parallel algorithm was designed on Giraph++ which is a semi-asynchronous parallel graph computation framework running on distributed environment. In the algorithm, a network of large size is firstly divided into a number of small sub-networks. Then, each sub-network is modeled as a self-evolving swarm intelligence sub-system, while each vertex within the sub-network acts iteratively to join into or leave from communities based on a set of predefined vertex action rules. Meanwhile, the local communities of a sub-network are sent to other sub-networks to make their members have a chance to join into, therefore connecting these self-evolving swarm intelligence sub-systems together as a whole, large and evolving, system. The vertex actions during evolution of a sub-network are sent as well to keep multiple community replicas being consistent. Thus network communication efficiency has a great impact on the algorithm’s performance. While there is no vertex changing in its belonging communities anymore, an optimal community structure of the whole network will have emerged as a result. In the algorithm it is natural that a vertex can join into multiple communities simultaneously, thus can be used for overlapping community detection. The algorithm deals with vertex and edge adding or deleting in the same way as the algorithm running, therefore inherently supports dynamic network analysis. The algorithm can be used for the analysis of large scale networks with its parallel version running on distributed environment. A variety of experiments conducted on synthesized networks have shown that the proposed algorithm can effectively detect community structures and its performance is much better than certain popular community detection algorithms

Learning Persistent Community Structures in Dynamic Networks via Topological Data Analysis

Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency regularization on inter-community structures, inspired by the concept of minimal network topological changes within short intervals. Specifically, to address the representation collapse problem, we first introduce MFC, a matrix factorization-based deep graph clustering algorithm that preserves node embedding. Based on static clustering results, we construct probabilistic community networks and compute their persistence homology, a robust topological measure, to assess structural similarity between them. Moreover, a novel neural network regularization TopoReg is introduced to ensure the preservation of topological similarity between inter-community structures over time intervals. Our approach enhances temporal consistency and clustering accuracy on real-world datasets with both fixed and varying numbers of communities. It is also a pioneer application of TDA in temporally persistent community detection, offering an insightful contribution to field of network analysis. Code and data are available at the public git repository: https://github.com/kundtx/MFC_TopoRegComment: AAAI 202

Incremental Measurement of Structural Entropy for Dynamic Graphs

Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal encoding tree corresponding to the optimal hierarchical community partitioning of the graph. However, the current structural entropy methods do not support efficient incremental updating of encoding trees. To address this issue, we propose Incre-2dSE, a novel incremental measurement framework that dynamically adjusts the community partitioning and efficiently computes the updated structural entropy for each snapshot of dynamic graphs. Incre-2dSE consists of an online module and an offline module. The online module includes dynamic measurement algorithms based on two dynamic adjustment strategies for two-dimensional encoding trees, i.e., the naive adjustment strategy and the node-shifting adjustment strategy, which supports theoretical analysis of the updated structural entropy and incrementally adjusts the community partitioning towards a lower structural entropy. In contrast, the offline module globally constructs the encoding tree for the updated graph using static community detection methods and calculates the structural entropy by definition. We conduct experiments on an artificial dynamic graph dataset generated by Hawkes Process and 3 real-world datasets. Experimental results confirm that our dynamic measurement algorithms effectively capture the dynamic evolution of the communities, reduce time consumption, and provide great interpretability

The Role of Prior Knowledge in Multi-Population Cultural Algorithms for Community Detection in Dynamic Social Networks

The relationship between a community and the knowledge that it encompasses is a fundamentally important aspect of any social network. Communities, with some level of similarity, implicitly tend to have some level of similarity in their knowledge as well. This work does the analysis on the role of prior knowledge in Multi-Population Cultural Algorithm (MPCA) for community detection in dynamic social networks. MPCA can be used to find the communities in a social network. The knowledge gained in this process is useful to analyze the communities in other social networks having some level of similarity. Our work assumes that knowledge is an integral part of any community of a social network and plays a very important role in its evolution. Different types of networks with levels of non-similarity are analyzed to see the role of prior knowledge while finding communities in them

Detecting users communities in mobile social networks

In this paper we focus on approaches which aim at discovering communities of people in Opportunistic Networks. We first study the behaviour of three community detection distributed algorithms proposed in literature [1], in a scenario where people move according to a mobility model which well reproduces the nature of human contacts, namely HCMM [2]. By a simulation analysis, we show that these distributed approaches can satisfactory detect the communities formed by people only when they do not significantly change over time. Otherwise, as they maintain memory of all encountered nodes forever, these algorithms fail to capture dynamic evolutions of the social communities users are part of. To this aim we propose AD-SIMPLE, a new solution which captures the dynamic evolution of social communities. By an extensive simulation analysis, we demonstrate that it accurately detects communities and social changes while keeping computation and storage requirements low

Linking Through Time: Memory-Enhanced Community Discovery in Temporal Networks

Temporal Networks, and more specifically, Markovian Temporal Networks, present a unique challenge regarding the community discovery task. The inherent dynamism of these systems requires an intricate understanding of memory effects and structural heterogeneity, which are often key drivers of network evolution. In this study, we address these aspects by introducing an innovative approach to community detection, centered around a novel modularity function. We focus on demonstrating the improvements our new approach brings to a fundamental aspect of community detection: the detectability threshold problem. We show that by associating memory directly with nodes' memberships and considering it in the expression of the modularity, the detectability threshold can be lowered with respect to cases where memory is not considered, thereby enhancing the quality of the communities discovered. To validate our approach, we carry out extensive numerical simulations, assessing the effectiveness of our method in a controlled setting. Furthermore, we apply our method to real-world data to underscore its practicality and robustness. This application not only demonstrates the method's effectiveness but also reveals its capacity to indirectly tackle additional challenges, such as determining the optimal time window for aggregating data in dynamic graphs. This illustrates the method's versatility in addressing complex aspects of temporal network analysis