Matrix notation for links networks

[Konard]

All possible links values

If we have a network of two links (with addresses 0 and 1) we can get all possible values for them:

(0 0)
(0 1)
(1 0)
(1 1)

Full links network description

(0: 0 0)
(1: 1 1)

(0: 1 1)
(1: 0 0)

According to links network definition, in order to have full description of network we have to define injective function to map all links addresses to their values.

Partial Equivalence

Two matrices with the same size are equivalent, even if different link addresses are used as rows and columns.
Therefore, there is no need to draw 82 columns and rows if all is matter to us is two links with concrete address.
We also can see here that we can easily swap any link address with another address. For example, on this picture 0 is swapped with 48, and 1 is swapped with 82.

Operations

Each matrix can represent a single links network state. Once we draw a transition between two states, we get an exact representation of operations.

Create operation

This picture shows the create operation.
If the cell for a link is empty, that means there is no link with this value in the network.
Create operation is the operation that increases the number of existing links.

Update operation

Update operation is the operation that keeps the number of existing links the same.
To get difference should ignore all links' values that are present in both states.

Delete operation

Delete operation is the operation that decreases the number of existing links.

This notation is similar to Adjacency matrix in ability to represent the existence of links. But is different on what is written on cells. Adjacency matrix has a sign of existence in each cell. The matrix notation for links network has a link's actual value in each cell.