A study of graph spectra for comparing graphs and trees

Wilson, Richard C.; Zhu, Ping

doi:10.1016/j.patcog.2008.03.011

Cited by 197 publications

(155 citation statements)

References 25 publications

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“…In [26], [27], it has been found that Laplacian representation of graphs is better than adjacency matrix when used to compare the cospectrality of graphs. As such, we first compute the Laplacian matrices, Λ, for each topology (i.e., Λ = D − A where D is the degree matrix where the elements in the principal diagonal encodes the degree of each node and A is the adjacency matrix).…”

Section: F Impact Of Different Topologiesmentioning

confidence: 99%

Providing Information Resilience Through Modularity-Based Caching in Perturbed Information-Centric Networks

Chai

Sourlas

Pavlou

2017

2017 29th International Teletraffic Congress (ITC 29)

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Abstract-In this paper, we investigate the provision of a new form of resilience, namely information resilience -targeting reliable communication of information under normal and adverse network conditions. We harness the power and flexibility of information-centric networking (ICN) paradigm where content are named and can be explicitly identified as opposed to the current host-centric Internet. Using ICN principles, a new modularity-based information caching approach is proposed that leverages the concept of modularity such that information reachability and persistency are enhanced especially under perturbed network scenarios, e.g., network failures due to natural disasters or network under malicious attacks. The main idea of our proposal is to exploit the better connectivity of nodes within certain community construct in a network to provide higher information diversity, and thus allow potential access to a higher number of information objects even under various network dynamics. We conduct extensive simulations based on both real and model network topologies and show that our proposal can significantly increase request satisfaction ratios under highly dynamic network scenarios (i.e., network under multiple perturbations) across different system parameters.

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Section: F Impact Of Different Topologiesmentioning

confidence: 99%

Providing Information Resilience Through Modularity-Based Caching in Perturbed Information-Centric Networks

Chai

Sourlas

Pavlou

2017

2017 29th International Teletraffic Congress (ITC 29)

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“…Wilson et al [28] employed eigenvectors of Laplacian matrix to construct permutation invariants to characterize graph structures. Wilson and Zhu [29] investigated combining eigenvalues of various graph matrix representations to summarize a graph structure. Shokoufandeh et al [20] explored an approach to using eigenvalues of the adjacency matrix of the directed acyclic graph to construct a topological signature for encoding hierarchical image structures.…”

Section: Related Workmentioning

confidence: 99%

“…On the one hand, the Laplacian spectra are much more natural and important than the adjacency spectra and contain more information [33]. And the normalized Laplacian spectra perform the best with respect to cospectrality according to the empirical study in [29]. On the other hand, the known spectral radius of the normalized Laplacian matrix is leveraged to construct a fixed size feature vector, which results in a well-formed descriptor and is beneficial for the potential research on feature learning [34]- [36].…”

Section: Related Workmentioning

confidence: 99%

A Local Structural Descriptor for Image Matching via Normalized Graph Laplacian Embedding

Tang

Shao

et al. 2016

IEEE Trans. Cybern.

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Abstract-This paper investigates graph spectral approaches to the problem of point pattern matching. Specifically, we concentrate on the issue of how to effectively use graph spectral properties to characterize point patterns in the presence of positional jitter and outliers. A novel local spectral descriptor is proposed to represent the attribute domain of feature points. For a point in a given point-set, weight graphs are constructed on its neighboring points and then their normalized Laplacian matrices are computed. According to the known spectral radius of the normalized Laplacian matrix, the distribution of the eigenvalues of these normalized Laplacian matrices is summarized as a histogram to form a descriptor. The proposed spectral descriptor is finally combined with the approximate distance order for recovering correspondences between point-sets. Extensive experiments demonstrate the effectiveness of the proposed approach and its superiority to the existing methods.Index Terms-Graph spectrum, local structural descriptor, normalized Laplacian matrix, point pattern matching (PPM).

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“…Two completely different graphs can have the same exact spectra. Furthermore, small structural differences can significantly influence the spectrum of the graph [22]. Nonetheless, spectral graph theory provides powerful methods to efficiently assess the structure of graphs.…”

Section: Spectral Graph Theorymentioning

confidence: 99%

Enhancing productivity with back-end similarity matching of digital circuits for IP reuse

Zeng

Athanas

2013

2013 International Conference on Reconfigurable Computing and FPGAs (ReConFig)

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(ABSTRACT)Productivity for digital circuit design is being outpaced currently by the rate at which silicon is growing such as FPGAs. Complex designs take a large amount of engineering hours to complete. Reuse of existing design can potentially decrease this cost and increase design productivity. However, existing digital hardware designs are not being effectively reused by the hardware community due to the inability of designers to have knowledge of all the attributes of designs that can be reused. In addition, designers will have to accustom themselves to designs in the hardware library. By having a back-end system that looks for similar circuits, there is little to no effort for the designer to reuse the design. This thesis provides an overview and comparison of different methods for characterizing and comparing digital circuits in order to suggest candidate circuits that engineers can reuse. Several of these methods are implemented, modified, and compared to show the feasibility of utilizing this work for increasing overall productivity.

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A study of graph spectra for comparing graphs and trees

Cited by 197 publications

References 25 publications

Providing Information Resilience Through Modularity-Based Caching in Perturbed Information-Centric Networks

Providing Information Resilience Through Modularity-Based Caching in Perturbed Information-Centric Networks

A Local Structural Descriptor for Image Matching via Normalized Graph Laplacian Embedding

Enhancing productivity with back-end similarity matching of digital circuits for IP reuse

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