A Dynamic Algorithm for Updating Katz Centrality in Graphs

Nathan, Eisha; Bader, David A.

doi:10.1145/3110025.3110034

Cited by 17 publications

(10 citation statements)

References 15 publications

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“…We extended our previous work in [1][2][3] by using dynamic algorithms for calculating centrality scores in order to find local communities in evolving networks.…”

Section: Discussionmentioning

confidence: 99%

“…For PageRank, we solve for the correction ∆c so that we can obtain the new solution at time t + 1 as c t+1 = c t + ∆c. The algorithm for updating Katz centrality is published in our previous work in [2] and the algorithm for updating PageRank is published in our previous work in [3].…”

Section: Methodsmentioning

confidence: 99%

“…We extend our previous work in [1][2][3] by applying it to the problem of local community detection, defined further in Section 3.1. Our work on updating PageRank and Katz Centrality are necessary steps towards tracking "relevant" subgraphs around seed vertices using personalized centrality metrics.…”

Section: Contributionsmentioning

confidence: 99%

“…In [3], we present an algorithm for updating PageRank values in dynamic graphs by only using sparse updates to the residual is presented. A similar algorithm for updating Katz centrality scores is given in [2].…”

Section: Dynamic Algorithms For Centrality Measuresmentioning

confidence: 99%

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Local Community Detection in Dynamic Graphs Using Personalized Centrality

et al. 2017

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Analyzing massive graphs poses challenges due to the vast amount of data available. Extracting smaller relevant subgraphs allows for further visualization and analysis that would otherwise be too computationally intensive. Furthermore, many real data sets are constantly changing, and require algorithms to update as the graph evolves. This work addresses the topic of local community detection, or seed set expansion, using personalized centrality measures, specifically PageRank and Katz centrality. We present a method to efficiently update local communities in dynamic graphs. By updating the personalized ranking vectors, we can incrementally update the corresponding local community. Applying our methods to real-world graphs, we are able to obtain speedups of up to 60× compared to static recomputation while maintaining an average recall of 0.94 of the highly ranked vertices returned. Next, we investigate how approximations of a centrality vector affect the resulting local community. Specifically, our method guarantees that the vertices returned in the community are the highly ranked vertices from a personalized centrality metric.

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“…We extended our previous work in [1][2][3] by using dynamic algorithms for calculating centrality scores in order to find local communities in evolving networks.…”

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Section: Dynamic Algorithms For Centrality Measuresmentioning

confidence: 99%

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Local Community Detection in Dynamic Graphs Using Personalized Centrality

et al. 2017

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“…Here the degree of nodes is adopted as the criterion of sorting neighbors in an ordered sequence for the reason that taking degree as measure for neighbor ordering is the most efficient and that degree is a crucial part in many graph-theoretic measures, notably those relating to structural roles, e.g. Katz [47] and PageRank [49].…”

Section: Recursive Embeddingmentioning

confidence: 99%

Deep Learning for Learning Graph Representations

Zhu

Wang

Cui

2019

Studies in Computational Intelligence

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Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data has posed great challenges for efficient analysis. This motivates the advent of graph representation which maps the graph into a low-dimension vector space, keeping original graph structure and supporting graph inference. The investigation on efficient representation of a graph has profound theoretical significance and important realistic meaning, we therefore introduce some basic ideas in graph representation/network embedding as well as some representative models in this chapter. them may have its own terminology, e.g., a vertice and an edge in a graph v.s. a node and a link in a network. Therefore we will exchangeably use graph representation and network embedding without further explanations in the remainder of this chapter. The core of mining graphs/networks relies heavily on properly representing graphs/networks, making representation learning on graphs/networks a fundamental research problem in both academia and industry. Traditional representation approaches represent graphs directly based on their topologies, resulting in many issues including sparseness, high computational complexities etc., which actuates the advent of machine learning based methods that explore the latent representations capable of capturing extra information in addition to topological structures for graphs in vector space. As such, the ability to find "good" latent representations for graphs plays an important role in accurate graph representations. However, learning network representations faces challenges as follows:1. High non-linearity. As is claimed by Luo et al. [43], the network has highly non-linear underlying structure. Accordingly, it is a rather challenging work to design a proper model to capture the highly non-linear structure.2. Structure-preserving. With the aim of supporting network analysis applications, preserving the network structure is required for network embedding. However, the underlying structure of the network is quite complex [55]. In that the similarity of vertexes depends on both the local and global network structure, it is a tough problem to preserve the local and global structure simultaneously.3. Property-preserving. Real-world networks are normally very complex, their formation and evolution are accompanied with various properties such as uncertainties and dynamics. Capturing these properties in graph representation is of significant importance and poses great challenges. 4. Sparsity. Real-world networks are often too sparse to provide adequate observed links for utilization, consequently causing unsatisfactory performances [50]. Many network embedding methods have been put forward, which adopt shallow models like IsoMAP [62], Laplacian Eigenmaps (LE) [4] and Line [61]. However, on account of the limited representation ability [6], it is challenging for them to captu...

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Centrality Measures: A Tool to Identify Key Actors in Social Networks

Singh

2021

Smart Innovation, Systems and Technologies

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A Dynamic Algorithm for Updating Katz Centrality in Graphs

Cited by 17 publications

References 15 publications

Local Community Detection in Dynamic Graphs Using Personalized Centrality

Local Community Detection in Dynamic Graphs Using Personalized Centrality

Deep Learning for Learning Graph Representations

Centrality Measures: A Tool to Identify Key Actors in Social Networks

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