The incidence matrix *A *has *m *= 6 rows and *n *= 4 columns. Each row corresponds

to an edge in the graph, and each column corresponds to a node. We do have to

number the edges and nodes, and also choose directions for the arrows, in order to

construct *A*. But the numbering and edge directions are arbitrary. Flows can travel

both ways, and a different choice of arrows will not change the reality of the model.

The entries *−*1 and 1 in each row of *A *give a record of the corresponding edge:

**Row 1**

The first edge leaves node 1 and goes to node 2.

The first row has *−*1 in column 1 and +1 in column 2.

Row 5 is typical. Edge 5 leaves node 2 (by *−*1 in column 2), and it enters node 4

(+1 in column 4). We chose arrows from lower-numbered nodes to higher-numbered

nodes, for simplicity. Then the *−*1 comes before the +1 in each row. In all cases, you

can write down *A *immediately by looking at the graph. The graph and the matrix

have the same information.