> For the complete documentation index, see [llms.txt](https://docs.enercalc.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.enercalc.com/e3d-user-manual/model-entities/toc161394020/toc161394023.md).

# Node Numbers

Understand how node numbering, gaps, and renumbering affect half band width and solution time.

A distinct integral number is assigned to each node. Node numbers are used to define the connectivity of member and finite elements. Duplicate numbers in nodes are not permitted. There can be gaps in node numbering sequence. The program will automatically renumber the nodes internally before performing the solution. The order of node numbering in a model is insignificant to the final results, but it may affect the time and computer memory required to solve the model. For a very large model, node renumbering may be important in order to reduce the half band width in the global stiffness matrix and therefore the solution time. You may renumber the nodes sequentially based on nodal coordinates using the command Edit > Renumber Nodes.

Half Band Width (HBW) is defined as \[Ref.7] as follows:

![](https://560001759-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWNe8U6EBBBdUJHdb2X9G%2Fuploads%2Fgit-blob-efd8b14aa80d7493978ce0f5cf34213f45e3b16c%2FHBW.jpg?alt=media)

where m is the total number of structural elements, and the max *dof\*\*el* and min *dof\*\*el* are the maximum and minimum global degrees of freedom numbers associated with element el.

For example, in the screen captures below, models A and B are identical 3D frames (6 DOFs per node) but with different node numbering schemes. Model A has a HBW of 6 \* (9 + 1) = 60 while model B has a HBW of 6 \* (5 + 1) = 36. Therefore, model B is more economical than model A because of the reduction of half band width.

| ![](https://560001759-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWNe8U6EBBBdUJHdb2X9G%2Fuploads%2Fgit-blob-1e8ec5acee0e10bdf165ecceac0f7f324eaf8507%2FFASTFR~1_img227.png?alt=media) Model A: HBW=60 | ![](https://560001759-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWNe8U6EBBBdUJHdb2X9G%2Fuploads%2Fgit-blob-1253ad8f5459ec7d7d0901b9418c360c57964f3a%2FFASTFR~1_img228.png?alt=media) Model B: HBW=36 |
| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |


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