1.2 Lecture 2. Incidence matrices

There are several ways of encoding graphs. We use the most straightforward one. Our notations are not standard, but will be kept throughout the course.

Given a graph, numerate its vertices:

$$A_1,\dots,A_{\alpha}.$$

Definition 1.2.1   The incidence matrix of a graph is the $\alpha\times\alpha$ matrix $m_{ij}$ with natural ^1.1 entries where

$$m_{ij}=$$number of edges joining $$A_i$$ and $$A_j.$$

The numbers $m_{ii}$ mean, of course, the number of loops based at $A_i$ .

Exercise 1.2.2   Number the vertices and compose the incidence matrix of some graphs from Example .