The term network is formally defined within graph theory, a branch of discrete mathematics, as a set of nodes (or "vertices") and links. A node in a network may be linked to an arbitrary number of other nodes.

The number of links for any one node is called its degree; e.g., a node with a degree of zero is not linked at all. Another simple formal property of a network is its order: the number of its nodes. You may make practical use of the degree of nodes by using it as a sorting criterion in the codes list window. The column 'Density' in the Code Manager represents the degree of a code.

Links are usually drawn as lines between the connected nodes in graphical presentations of networks.

Furthermore, a link between two nodes may be directed or not. A directed connection is drawn with an arrow. With directed links, source and target nodes must be distinguished. The source node is where the link starts, and the target node is where it ends: the destination to which the arrow points.

Links are created either implicitly (e.g., when coding a quotation, the quotation is "linked" to a code), or explicitly by the user. See Linking Nodes.

Strictly speaking, code-quotation associations ("codings") also form a network. However, you cannot name these links, the code is simply associated with a quotation through the act of coding. In a network you can visualize these links. In ATLAS.ti all unnamed links are referred to as second class links, all named links are referred to as first-class links.

First-class links are links based on relations. They are entities by themselves, with names, authors, comments, and other properties. They are available for:

• Links between two codes. These include:

• links between two category codes
• links between two subcodes (within or across categories)
• links between a subcode and its own or other category codes

Second-class links are links that do not have individual properties; These are:

• links between quotations and codes

• all links between a group and its members

• links between categories and their subcodes
• links between folders and categories
• links between folders and independent codes
• links between folders and subcodes

If you change hierarchical links in the network, this has an effect on the hierarchy of codes and folders in the entire your project!

## Why Groups Cannot be Linked

Groups cannot be linked as by definition, they are not mutually exclusive. You can add a document to as many document groups as you want. This also applies to code groups. A code can be a member of multiple code groups.

Groups are filters. Code groups are at times regarded by users as a higher order category, which they are not. See Building a Code System for further detail.

In order to compare and analyze documents by certain criteria like sociodemographic characteristics, you add them to document groups like gender::male / female, family status::single / married / separated / divorced, etc. This allows you also to combine certain criteria, e.g., to run an analysis for all female respondents that are married. See Working with document groups and Working with Smart Groups.

Likewise, the purpose of code groups is to be used as filters. A useful filter could be all codes of a category, but also all codes that are relevant for a certain research questions, or all codes that could be classified as coding a strategy, or a consequence or a context across different categories.

So you might have a code group containing codes A, B, C and D, and another code group containing codes B, D, E and F. If you now were to relate these two code groups to each other, you end up with circular or illogical relations.