A new area of study called "neutrosophic graph theory" uses neutrosophic logic to expand on traditional graph theory to include ambiguous, indeterminate, and uncertain information. This paper gives a thoroug...
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The world of industry has increasingly complex efficient machines and installations, the fault detection and isolation procedure is an essential module used to guarantee the continued functioning of the systems in the...
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Betweenness centrality has been extensively studied since its introduction in 1977 as a measure of node importance in graphs. This measure has found use in various applications and has been extended to temporal graphs...
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Betweenness centrality has been extensively studied since its introduction in 1977 as a measure of node importance in graphs. This measure has found use in various applications and has been extended to temporal graphs with time-labeled edges. Recent research by Bu ss et al. and Rymar et al. has shown that it is possible to compute the shortest walks betweenness centrality of all nodes in a temporal graph in On3T2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( n<^>3\,T<^>2\right)$$\end{document} and On2mT2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( n<^>2\,m\,T<^>2\right)$$\end{document} time, respectively, where T is the maximum time, m is the number of temporal edges, and n is the number of nodes. These approaches considered walks that do not take into account contributions from intermediate temporal nodes. In this paper, we study the temporal betweenness centrality on classical walks that we call passive, as well as on a variant that we call active walks, which takes into account contributions from all temporal nodes. We present an improved analysis of the running time of the classical algorithm for computing betweenness centrality of all nodes, reducing the time complexity to OnmT+n2T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( n\,m\,T+ n<^>2\,T\right)$$\end{document}. Furthermore, for active walks, we show that the betweenness centrality can be computed in OnmT+n2T2\documentclass[12pt]{minimal} \u
The Kirchhoff index, which is the sum of the resistance distance between every pair of nodes in a network, is a key metric for gauging network performance, where lower values signify enhanced performance. In this pape...
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The digital world has given rise to massive quantities of data that include rich semantic and complex networks. A social graph, for example, containing hundreds of millions of actors and tens of billions of relationsh...
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The digital world has given rise to massive quantities of data that include rich semantic and complex networks. A social graph, for example, containing hundreds of millions of actors and tens of billions of relationships is not uncommon. Analyzing these large data sets, even to answer simple analytic queries, often pushes the limits of algorithms and machine architectures. We present graphCT, a scalable framework for graph analysis using parallel and multithreaded algorithms on shared memory platforms. Utilizing the unique characteristics of the Cray XMT, graphCT enables fast network analysis at unprecedented scales on a variety of input data sets. On a synthetic power law graph with 2 billion vertices and 17 billion edges, we can find the connected components in 2 minutes. We can estimate the betweenness centrality of a similar graph with 537 million vertices and over 8 billion edges in under 1 hour. graphCT is built for portability and performance.
Community detection is a commonly encountered problem in social network analysis and many other areas. A community in a graph or network is a subgraph containing vertices that are closely connected to other vertices w...
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ISBN:
(纸本)9783031785375;9783031785382
Community detection is a commonly encountered problem in social network analysis and many other areas. A community in a graph or network is a subgraph containing vertices that are closely connected to other vertices within the same subgraph but have fewer connections to the other vertices. Community detection is useful in analyzing complex systems and recognizing underlying patterns and structures that govern them. There are several algorithms that currently exist for community detection, ranging from simple and fast approaches, such as the label propagation algorithm (LPA), to more complex and time-consuming methods, such as the state-of-the-art Louvain method. We propose a new method called vector label propagation (VLP), which is a generalization of the LPA approach. The VLP algorithm significantly enhances the quality of the detected communities compared to LPA while being much faster than the Louvain method. For example, on the Twitter network, VLP has a normalized mutual information (NMI) score of 0.82, while LPA has an NMI score of 0.47. With rigorous experimentations, we demonstrate that the VLP algorithm is significantly faster than state-of-the-art algorithms such as Louvain and Infomap. On the Twitter network, VLP is 2.8 times faster than Louvain.
When enough people leave a project, the project might stall due to lack of knowledgeable personnel. The minimum number of people who are required to disappear in order for a project to stall is referred to as bus-fact...
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ISBN:
(纸本)9783031785405;9783031785412
When enough people leave a project, the project might stall due to lack of knowledgeable personnel. The minimum number of people who are required to disappear in order for a project to stall is referred to as bus-factor. The bus-factor has been found to be real and tangible and many approaches to measure it have been developed. These approaches are problematic: some of them do not scale to large projects, others rely on ad-hoc notions of primary and secondary developers, and others use arbitrary thresholds. None of them proposes a normalized measure of the bus-factor. Therefore, in this paper we propose a framework that, by modelling a project with a bipartite graph linking people to tasks, allows us to 1) quantify the bus-factor of a project with a normalized measure which does not rely on thresholds;and 2) increase the bus-factor of a project by reassigning people to tasks. We demonstrate our approach on a real case, discuss the advantages of our framework, and outline possibilities for future research.
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands ...
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Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus, increasing the complexity of their analysis. Vector search is the backbone of many critical analytical tasks, and graph-based methods have become the best choice for analytical tasks that do not require guarantees on the quality of the answers. We briefly survey in-memory graph-based vector search, outline the chronology of the different methods and classify them according to five main design paradigms: seed selection, incremental insertion, neighborhood propagation, neighborhood diversification, and divide-and-conquer. We conduct an exhaustive experimental evaluation of twelve state-of-the-art methods on seven real data collections, with sizes up to 1 billion vectors. We share key insights about the strengths and limitations of these methods; e.g., the best approaches are typically based on incremental insertion and neighborhood diversification, and the choice of the base graph can hurt scalability. Finally, we discuss open research directions, such as the importance of devising more sophisticated data-adaptive seed selection and diversification strategies.
Mining graphs, upon query, for k shortest paths between vertex pairs is a prominent primitive to support several analytics tasks on complex networked datasets. The state-of-the-art method to implement this primitive i...
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ISBN:
(纸本)9783031785405;9783031785412
Mining graphs, upon query, for k shortest paths between vertex pairs is a prominent primitive to support several analytics tasks on complex networked datasets. The state-of-the-art method to implement this primitive is KPLL, a framework that provides very fast query answering, even for large inputs and volumes of queries, by pre-computing and exploiting an appropriate index of the graph. However, if the graph's topology undergoes changes over time, such index might become obsolete and thus yield incorrect query results. Re-building the index from scratch, upon every modification, induces unsustainable time overheads, incompatible with applications using k shortest paths for analytics purposes. Motivated by this limitation, in this paper, we introduce DECKPLL, the first dynamic algorithm to maintain a KPLL index under decremental modifications. We assess the effectiveness and scalability of our algorithm through extensive experimentation and show it updates KPLL indices orders of magnitude faster than the re-computation from scratch, while preserving its compactness and query performance. We also combine DECKPLL with INCKPLL, the only known dynamic algorithm to maintain a KPLL index under incremental modifications, and hence showcase, on real-world datasets, the first method to support fast extraction of k shortest paths from graphs that evolve by arbitrary topological changes.
Accurate timing verification and optimization methods require algorithms that exclude false paths. Recently published methods for critical path searches that eliminate false paths, can take long evaluation times for c...
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Accurate timing verification and optimization methods require algorithms that exclude false paths. Recently published methods for critical path searches that eliminate false paths, can take long evaluation times for complex time-optimized circuits. In this paper a new
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