Changes

Nodes in a graph represent ''records'' in computer memory.  A record is a collection of data that can be conceived to reside at a specific ''address''.  The address of a record is analogous to a demonstrative pronoun, on which account programmers commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

Nodes in a graph represent ''records'' in computer memory.  A record is a collection of data that can be conceived to reside at a specific ''address''.  The address of a record is analogous to a demonstrative pronoun, on which account programmers commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

At the next level of concreteness, a pointer→record data structure can be represented as follows:

At the next level of concreteness, a pointer-record structure may be represented as follows:

{| align="center" border="0" cellpadding="10" cellspacing="0"

{| align="center" cellpadding="10"

| [[Image:Logical_Graph_Figure_11_Visible_Frame.jpg|500px]] || (11)

| [[Image:Logical_Graph_Figure_11_Visible_Frame.jpg|500px]] || (11)

|}

|}

This portrays <math>index_0\!</math> as the address of a record that contains the following data:

This portrays the pointer <math>\operatorname{index}_0</math> as the address of a record that contains the following data:

<center><p><math>datum_1, datum_2, datum_3, \ldots,\!</math> and so on.</p></center>

{| align="center" cellpadding="10"

| <math>\operatorname{datum}_1, \operatorname{datum}_2, \operatorname{datum}_3, \ldots,</math> and so on.

What makes it possible to represent graph-theoretical structures as data structures in computer memory is the fact that an address is just another datum, and so we may have a state of affairs like the following:

What makes it possible to represent graph-theoretical structures as data structures in computer memory is the fact that an address is just another datum, and so we may have a state of affairs like the following:

{| align="center" border="0" cellpadding="10" cellspacing="0"

{| align="center" cellpadding="10"

| [[Image:Logical_Graph_Figure_12_Visible_Frame.jpg|500px]] || (12)

| [[Image:Logical_Graph_Figure_12_Visible_Frame.jpg|500px]] || (12)

|}

|}

Returning to the abstract level, it takes three nodes to represent the three data records illustrated above:  one root node connected to a couple of adjacent nodes.  The items of data that do not point any further up the tree are then treated as labels on the record-nodes where they reside, as shown below:

Returning to the abstract level, it takes three nodes to represent the three data records illustrated above:  one root node connected to a couple of adjacent nodes.  The items of data that do not point any further up the tree are then treated as labels on the record-nodes where they reside, as shown below:

{| align="center" border="0" cellpadding="10" cellspacing="0"

{| align="center" cellpadding="10"

| [[Image:Logical_Graph_Figure_13_Visible_Frame.jpg|500px]] || (13)

| [[Image:Logical_Graph_Figure_13_Visible_Frame.jpg|500px]] || (13)

|}

|}