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Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.


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Journal ArticleDOI
TL;DR: The effect on the spectra of hubs in the network, vertices of unusually high degree, are studied, and it is shown that these produce isolated eigenvalues outside the main spectral band, akin to impurity states in condensed matter systems.
Abstract: We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit of large network size and large vertex degrees. We also study the effect on the spectra of hubs in the network, vertices of unusually high degree, and show that these produce isolated eigenvalues outside the main spectral band, akin to impurity states in condensed matter systems, with accompanying eigenvectors that are strongly localized around the hubs. We give numerical results that confirm our analytic expressions.

80 citations

Journal ArticleDOI
TL;DR: It is shown that in many instances this adjacency matrix is superior to the usual (0, 1) adjacencies, and will distinguish cospectral pairs, when the latter will not.

77 citations

Journal ArticleDOI
01 Sep 1998
TL;DR: The paper describes SAGE, a software system that can undertake exploratory spatial data analysis (ESDA) held in the ARC/INFO geographical information system and describes the interaction between the table, map and graph drawing windows in SAGE.
Abstract: The paper describes SAGE, a software system that can undertake exploratory spatial data analysis (ESDA) held in the ARC/INFO geographical information system. The aims of ESDA are described and a simple data model is defined associating the elements of ‘rough’ and ‘smooth’ with different attribute properties. The distinction is drawn between global and local statistics. SAGE's region building and adjacency matrix modules are described. These allow the user to evaluate the sensitivity of results to the choice of areal partition and measure of interarea adjacency. A range of ESDA techniques are described and examples given. The interaction between the table, map and graph drawing windows in SAGE is illustrated together with the range of data queries that can be implemented based on attribute values and locational criteria. The paper concludes with a brief assessment of the contribution of SAGE to the development of spatial data analysis.

77 citations

Proceedings ArticleDOI
27 Jun 2007
TL;DR: Experimental results on a variety of challenging kinodynamic motion planning problems show computational speedups of two orders of magnitude over other widely used motion planning methods.
Abstract: This paper presents the Discrete Search Lead- ing continuous eXploration (DSLX) planner, a multi-resolution approach to motion planning that is suitable for challenging problems involving robots with kinodynamic constraints. Initially the method decomposes the workspace to build a graph that encodes the physical adjacency of the decomposed regions. This graph is searched to obtain leads, that is, sequences of regions that can be explored with sampling-based tree methods to generate solution trajectories. Instead of treating the discrete search o f the adjacency graph and the exploration of the continuous state space as separate components, DSLX passes information from one to the other in innovative ways. Each lead suggests what regions to explore and the exploration feeds back information to the discrete search to improve the quality of future leads. Information is encoded in edge weights, which indicate the importance of including the regions associated with an edge in the next exploration step. Computation of weights, leads, and the actual exploration make the core loop of the algorithm. Extensive experimentation shows that DSLX is very versatile. The discrete search can drastically change the lead to reflect new information allowing DSLX to find solutions even when sampling-based tree planners get stuck. Experimental results on a variety of challenging kinodynamic motion planning problems show computational speedups of two orders of magnitude over other widely used motion planning methods.

77 citations

Journal ArticleDOI
TL;DR: This work shows that any list edge-coloring can be transformed into any other under the sufficient condition that the number of allowed colors for each edge is strictly larger than the degrees of both its endpoints.

77 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023209
2022439
2021283
2020280
2019296
2018232