本文深入探讨了图论的基本概念，包括节点、边以及它们如何构成图。通过一个包含4个节点和5条边的具体例子，详细展示了如何使用矩阵来表示图的结构，解释了1和-1在矩阵中分别代表流入和流出节点的概念。此外，还讨论了生成树和独立行在图论中的应用。
Description
- A Graph consists of a set of nodes, and a set of edges that connect them
Examples
- The graph below has 4 nodes and 5 edges
The Graph above can be expressed by matrix as this :
A=[−1100−10100−1100−10100−11]
A= \left[
\begin{matrix}
-1 & 1 & 0 &0& \\
-1 & 0 & 1 &0&\\
0 & -1 & 1 &0&\\
0 & -1 & 0 &1&\\
0 & 0 & -1 &1&
\end{matrix}
\right]
A=⎣⎢⎢⎢⎢⎡−1−100010−1−100110−100011⎦⎥⎥⎥⎥⎤
- each column represents a node and each row represents an edge.
- 1 means flowing into that node. -1 ,on the contraty ,means flowing out that node
Spanning Trees and Independent Rows
The procession of elimination mostly seems kind of like cut loops .
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