V2EX incidence matrix

Incidence Matrix

释义 Definition

关联矩阵 / 关联矩阵(图论):在图论中,用一个矩阵表示“顶点边”的关联关系。常见定义是:行对应顶点(vertices),列对应边(edges);若某条边与某个顶点相连,则对应位置取 1(或在有向图中用 +1/1 表示方向),否则为 0。
(该术语在不同教材中可能有细微约定差异,如无向图用 0/1,有向图用 1/0/+1。)

发音 Pronunciation (IPA)

/nsdns metrks/

例句 Examples

An incidence matrix shows which vertices each edge touches.
关联矩阵展示每条边与哪些顶点相连接。

Using the incidence matrix, we can translate the graph problem into linear algebra and compute flows more efficiently.
利用关联矩阵,我们可以把图问题转化为线性代数问题,从而更高效地计算网络流等量。

词源 Etymology

incidence 源自拉丁语 incidere(“落在……上、发生、相交”),强调“相交/关联”的关系;matrix 源自拉丁语 matrix(“母体、源头”),在数学中引申为“矩阵”。合起来,incidence matrix 就是“用矩阵表达关联关系”的意思。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Graph Theory Reinhard Diestel(图论经典教材,讨论关联矩阵与图的表示)
  • Introduction to Graph Theory Douglas B. West(入门教材,常用矩阵方法表示图)
  • Algebraic Graph Theory Chris Godsil & Gordon Royle(代数图论中频繁使用各种图矩阵,包括关联矩阵)
  • Networks, Crowds, and Markets David Easley & Jon Kleinberg(网络分析背景下涉及图的矩阵表示方法)
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