Vertex-Cut Partitioning Performance Analysis for FASTCD Algorithm in Large-Scale Graph

This thesis delves into critical challenges associated with subgraph analysis in large-scale graphs. The proliferation of data in domains such as social networks, Internet applications, and biological networks necessitates a deep understanding of relationships modeled as graphs. The complexity and scale of these graphs pose challenges for efficient extraction of meaningful information. The thesis focuses on three interconnected research problems: subgraph counting in fully-dynamic graph streams, k-clique listing in large general graphs, and maximal clique enumeration in large general graphs. The first research problem addresses subgraph counting in fully-dynamic graph streams, where graphs evolve dynamically with edge insertions and deletions. Traditional ap- proaches sample edges uniformly, overlooking the varying importance of edges. The thesis introduces a novel weighted sampling framework, WSD, for fully-dynamic graph streams, which samples the edges based on their weights that indicate their importance and reflect their properties. It determines the weights of edges in a data-driven fashion, using a novel method based on reinforcement learning. We conduct extensive experi- ments to verify that our technique can produce estimates with smaller errors while often running faster compared with existing algorithms. The second research problem focuses on k-clique listing in large general graphs, a critical task for applications such as community detection and network analysis. The state-of-the-art algorithms all adopt a branch-and-bound (BB) framework with a vertex-oriented branching strategy (called VBBkC), which forms a sub-branch by expanding a partial k-clique with a vertex. These algorithms have the time complexity of O(km(\delta/2)^(k-2)), where m is the number of edges in the graph and \delta is the degeneracy of the graph. In this thesis, we propose a BB framework with a new edge-oriented branching (called EBBkC), which forms a sub-branch by expanding a partial k-clique with two vertices that connect each other (which correspond to an edge). We explore various edge orderings for EBBkC such that it achieves a time complexity of O(m\delta + km(\tau/2)^(k-2), where \tau is an integer related to the maximum truss number of the graph and we have \tau<\delta. The time complexity of EBBkC is better than that of VBBkC algorithms for k>3 since both O(m\delta) and O(km(\tau/2)^(k-2) are bounded by O(km(\delta/2)^(k-2)). Furthermore, we develop specialized algorithms for sub-branches on dense graphs so that we can early-terminate them and apply the specialized algorithms. We conduct extensive experiments on 19 real graphs, and the results show that our newly developed EBBkC based algorithms with the early termination technique consistently and largely outperform the state-of-the- art (VBBkC based) algorithms. The third research problem centers on maximal clique enumeration (MCE) in large general graphs, crucial for tasks like community detection and biological network analysis. Existing algorithms typically adopt the branch-and-bound framework with the vertex-oriented Bron-Kerbosch (BK) branching strategy, which forms the sub-branches by expanding the partial clique with a vertex. The state-of-the-arts have a time complexity no better than O(n\delta 3^(\delta/3)), where n is the number of vertices in the graph and \delta is the degeneracy of the graph. We introduce a novel approach, HBBMC, a hybrid framework combining vertex-oriented and edge-oriented BK branching, where the latter adopts a new branch-and-bound framework which forms the sub-branches by expanding the partial clique with a edge. This hybrid strategy enables more efficient pruning of sub-branches, resulting in a worst-case time complexity of O(m\delta + m\tau 3^(\tau/3)), where \tau is related to the maximum truss number. This theoretical result is better than that of the state-of-the-arts when \delta > \tau + (3/ln3) \rho, a condition satisfied by many real-world graphs, where \rho is the edge density of the graph defined as \rho = m/n. To further enhance efficiency, we introduce an early termination technique applicable to all branch-and-bound frameworks, which leverages the topological information of the graphs within the branches. This technique accelerates the enumeration process without affecting worst-case time complexity. Extensive experiments on real and synthetic graphs demonstrate the superior performance of our approach. The proposed HBBMC algorithm with the early termination technique consistently outperforms existing vertex-oriented algorithms. In summary, this thesis makes significant contributions by introducing novel algo- rithms, frameworks, and methodologies to address subgraph-related problems. The pro- posed approaches show superior performance across various real-world and synthetic datasets, providing efficient solutions for graph analysis in large-scale, dynamic, and complex scenarios.

We present a parallel hierarchical graph clustering algorithm that uses modularity as clustering criteria to effectively extract community structures in large graphs of different types. In order to process a large complex graph (whose vertex number and edge number are around 1 billion), we design our algorithm based on the Louvain method by investigating graph partitioning and distribution schemes on distributed memory architectures and conducting clustering in a divide-and-conquer manner. We study the relationship between graph structure property and clustering quality, carefully deal with ghost vertices between graph partitions, and propose a heuristic partition method suitable for the Louvain method. Compared to the existing solutions, our method can achieve nearly well-balanced workload among processors and higher accuracy of graph clustering on real-world large graph datasets.

Next generation analytics will be all about graphs, though performance has been a fundamental challenge for large scale graph processing. In this paper, we present an industrial graph processing engine for exploring various large scale linked data, which exhibits superior performance due to the several innovations. This engine organizes a graph as a set of edge-sets, compatible with the traditional edge-centric sharding for graphs, but becomes more amenable for large scale processing. Each time only a portion of the sets are needed for computation and the data access patterns can be highly predictable for prefetch for many graph computing algorithms. Due to the sparsity of large scale graph structure, this engine differentiates logical edge-sets from the edge-sets physically stored on the disk, where multiple logical edge-sets can be organized into a same physical edge-set to increase the data locality. Besides, in contrast to existing solution, the data structures utilized for the physical edge-sets can vary from one to another. Such heterogeneous edge-set representation explores the best graph processing performance according to local data access patterns. We conduct experiments on a representative set of property graphs on multiple platforms, where the proposed system outperform the baseline systems consistently.

How to efficiently detect communities for dynamic graphs has attracted significant attention due to its widespread applications, such as "Recommended System" in social networking or "Anti-Money Laundry" for banks. However, with the growing size and the increasing of changing frequency for dynamic graphs, it is better to detect communities incrementally than applying community detection algorithm for each of the graph. In this paper, we propose a generalized bottom-up community detection framework to help standard community detection algorithms to detect communities in highly dynamic graphs incrementally. The evaluations on real data sets show that our generalized framework does have the ability to accelerate standard community detection methods for highly dynamic graphs (up to 96%). In addition, for super hubs in large scale graph, we also propose an approximate process to meet the requirement of real-time processing. By giving "mathematical proof", "efficiency" and "accuracy" evaluations from real data sets, we demonstrate this approximate process can not only accelerate the community detection process but also can preserve the accuracy, as the normalized mutual information for regular communities and approximate communities is larger than 92%.

A New Randomized Algorithm for Community Detection in Large Networks

Graph data structures model relations between entities in various domains. Graph processing systems enable scalable distributed computations over large graphs, but are limited to static scenarios in which the structure of the graph does not change. However, many applications are dynamic in nature, and this reflects to graphs that continuously evolve over time. In these contexts, understanding the evolution of graphs is key to enable timely reactions when necessary. We address this problem by proposing a new model to express temporal patterns over graph data structures. The model seamlessly integrates computations over graphs to extract relevant values, and temporal operators that define patterns of interest in the evolution of the graph. We present the syntax and semantics of our model and discuss its concrete implementation in FlowGraph, a middleware for temporal pattern recognition in large scale graphs. FlowGraph presents a level of performance that is comparable to state-of-the-art graph processing tools when processing static graphs. In the presence of temporal patterns, it can further optimize processing by avoiding complex graph computations until strictly necessary for pattern evaluation.

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

Large graph analysis has become a widely studied area in recent years. Clustering is one of the most important types of analysis that has versatile applications such as community detection in social networks, image segmentation, graph partitioning, etc. However, existing clustering algorithms do not intend for large scale graphs. To solve this problem, we implemented spectral clustering in X10, that is a programming language aimed for developing highly scalable applications on Post- Petascale supercomputers. Our spectral clustering is based on the algorithm proposed by Shi and Malik. After evaluating scalability and precision, we found that our implementations are scalable in terms of execution time and precise for analyzing real data.

&lt;p dir="ltr"&gt;One of the most critical features of real-world networks is their community structure, as it reveals the internal organization of nodes. Finding such partitions is an interesting and essential task from both theoretical and practical perspectives. As a result, there is a growing demand for effective community detection algorithms. However, testing and designing such algorithms is demanding and challenging: one of the biggest problems is the lack of proper datasets and the fact that some have disputable ground-truth labeling, to say the least. One way to avoid this problem is to use artificial benchmarks with a built-in community structure.&lt;/p&gt;&lt;p dir="ltr"&gt;In this work, we propose ABCDe—a multi-threaded implementation of the ABCD (Artificial Benchmark for Community Detection) graph generator. We test its performance and compare it with the previously available sequential version of the ABCD model and the parallel implementation of the standard and widely used LFR generator. We also investigate various theoretical asymptotic properties of the ABCD and ABCDe models. In particular, we analyze the modularity function, arguably the most important graph property in the context of community detection. By doing so, we show that models from the ABCD family are proper tools for designing new algorithms, not only those suited specifically for the community detection task.&lt;/p&gt;&lt;p dir="ltr"&gt;Finally, we introduce a new approach to community detection in graphs. The idea is to initialize one of the popular heuristic-based community detection algorithms, such as Louvain or Leiden, with a partition obtained by embedding the graph nodes into a high-dimensional real vector space and then running a clustering algorithm on this latent representation. This procedure significantly improves the results and reduces the inherent volatility of such algorithms. Proper embedding filters out unnecessary information while retaining the proximity of nodes belonging to the same community.&lt;/p&gt;

Fast processing graph algorithms for large-scale graphs becomes increasingly important. Besides, there have been many attempts to process graph applications by exploiting the massive amount of parallelism of GPUs. However, most of the existing methods fail to process large-scale graphs that do not fit in GPU device memory. We propose a fast and scalable parallel processing method GStream that fully exploits the computational power of GPUs for processing large-scale graphs (e.g., billions vertices) very efficiently. It exploits the concept of nested-loop theta-join and multiple asynchronous GPU streams. Extensive experimental results show that GStream consistently and significantly outperforms the state-of-the art method.

The task of community detection in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches community detection in graphs by constructing Markov random walks on the graphs. The mixing properties of the random walk are then used to identify communities. We use coupling from the past as an algorithmic primitive to translate the mixing properties of the walk into revealing the community structure of the graph. We analyze the performance of our algorithms on specific graph structures, including the stochastic block models (SBM) and LFR random graphs.

Mining large-scale graphs is increasingly important, as it provides a powerful way of extracting useful information from real-world data. Efficient processing of that volume of information requires partitioning the graph across multiple nodes in a distributed system. However, traversing edges across distributed partitions results in significant performance penalty due to the additional cost of inter-partition communication. Minimising the number of cut edges between partitions improves communication cost between neighbouring vertices; balanced graph partitioning is required for load balancing [2].

Community detection is an advanced graph operation that is used to reveal tightly-knit groups of vertices (aka. communities) in real-world networks. Given the intractability of the problem, efficient heuristics are used in practice. Yet, even the best of these state-of-the-art heuristics can become computationally demanding over large inputs and can generate workloads that exhibit inherent irregularity in data movement on manycore platforms. In this paper, we posit that effective acceleration of the graph community detection operation can be achieved by reducing the cost of data movement through a combined innovation at both software and hardware levels. More specifically, we first propose an efficient software-level parallelization of community detection that uses approximate updates to cleverly exploit a diminishing returns property of the algorithm. Secondly, as a way to augment this innovation at the software layer, we design an efficient Wireless Network on Chip (WiNoC) architecture that is suited to handle the irregular on-chip data movements exhibited by the community detection algorithm under both unicast- and broadcast-heavy cache coherence protocols. Experimental results show that our resulting WiNoC-enabled manycore platform achieves on average 52% savings in execution time, without compromising on the quality of the outputs, when compared to a traditional manycore platform designed with a wireline mesh NoC and running community detection without employing approximate updates.

Community detection in graphs can be viewed as the estimation of a partition map that remains stable under admissible perturbations of graph topology and node attributes. While modern graph neural networks (GNNs) achieve strong empirical accuracy, they often exhibit severe assignment drift under minor perturbations, leading to illusory community structures. In this work, we propose DISPEL-GNN, a stability-aware graph learning framework that integrates spectral operator regularization, Bayesian uncertainty modeling, and risk-aware dynamic attention for perturbation-bounded community detection. The model explicitly constrains graph operators through uniform spectral norm bounds, high-frequency energy suppression, and commutator alignment while dynamically modulating message passing based on node-level spectral risk and epistemic uncertainty. We further formalize instability via assignment of drift functional and establish perturbation bounds linking drift to operator norms and spectral gaps, complemented by a PAC-Bayesian generalization guarantee. Extensive experiments on real-world benchmarks including Cora, Citeseer, Pubmed, Cora-Full, and DBLP demonstrate that DISPEL-GNN consistently reduces assignment drift by 18–35% under feature noise and edge perturbations while improving clustering quality with up to +3.0 NMI and +0.04 ARI compared to strong baselines such as GAT and Bayesian GNNs. The normalized mutual information (NMI), adjusted Rand index (ARI), and PAC-Bayesian (PAC) constraints serve as evaluative and theoretical instruments in this study. Additional studies on synthetic graphs with controlled spectral gaps confirm that the proposed method maintains stable community assignments in low-gap regimes where classical spectral and GNN-based methods degrade sharply. These results establish DISPEL-GNN as a mathematically grounded and practically effective framework for robust and interpretable community detection. A metric-wise dominance analysis shows that DISPEL-GNN achieves metric-wise dominance across most accuracy and robustness criteria, with minor tradeoffs in modularity on selected datasets. These results indicate that explicitly modeling stability and uncertainty provides a principled pathway toward reliable and interpretable community detection in noisy graph environments.

In the last years, large-scale graph processing has gained increasing attention, with most recent systems placing particular emphasis on latency. One possible technique to improve runtime performance in a distributed graph processing system is to reduce network communication. The most notable way to achieve this goal is to partition the graph by minimizing the number of edges that connect vertices assigned to different machines, while keeping the load balanced. However, real-world graphs are highly dynamic, with vertices and edges being constantly added and removed. Carefully updating the partitioning of the graph to reflect these changes is necessary to avoid the introduction of an extensive number of cut edges, which would gradually worsen computation performance. In this paper we show that performance degradation in dynamic graph processing systems can be avoided by adapting continuously the graph partitions as the graph changes. We present a novel highly scalable adaptive partitioning strategy, and show a number of refinements that make it work under the constraints of a large-scale distributed system. The partitioning strategy is based on iterative vertex migrations, relying only on local information. We have implemented the technique in a graph processing system, and we show through three real-world scenarios how adapting graph partitioning reduces execution time by over 50% when compared to commonly used hash-partitioning.