用空洞方法近似测定异构结构图的光谱密度
Grover E C Guzman1, Peter F Stadler2, Andre Fujita3
1Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, São Paulo - SP 05508-090, Brazil.
Physical review. E
|April 18, 2024
概括
本研究介绍了通过近似光谱密度来分析大型复杂图的高效方法. 新的基于腔的方法处理异质结构,克服了社会,生物和技术系统的先前技术的局限性.
科学领域:
- 图形理论是指图形的理论.
- 网络分析 网络分析
- 计算数学是指计算数学.
背景情况:
- 图形对于建模复杂系统 (社会,生物,技术) 是至关重要的.
- 光谱密度分析对于实证图表至关重要,但现有的方法在计算上昂贵 (立方时间复杂性).
- 空腔方法有效地分析稀疏的,局部树状的图形,但在现实世界网络中常见的异质结构中失败.
研究的目的:
- 开发高效的算法来计算大型异质图的光谱密度.
- 扩展空腔方法以适应复杂的,非树状的图形结构.
- 为各种科学领域的网络分析提供可扩展的工具.
主要方法:
- 为非定向和定向异质图提出了基于空腔的新方法.
- 引入了顶点局部邻近的新定义,以捕捉异质结构.
- 分析的时间和空间复杂度分别为O ((((((((((((((((
主要成果:
- 新的方法有效地近似异构结构的图形的光谱密度.
- 在模拟和现实世界的无定向和定向图形数据集上证明了实际有效性.
- 与现有的立方时算法相比,实现了显著的计算改进.
结论:
- 开发的方法为分析大型复杂网络中的光谱密度提供了可扩展和高效的解决方案.
- 这些算法适用于各种科学学科的广泛的经验图形.
- 这项工作通过研究以前难以处理的图形结构来推进网络分析.
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