Since I suggested that anybody who  is trying to define anything should check 
the definitions in a good dictionary, I decided to take my own advice.  See the 
attached defs.htm for definitions of the words 'diagram' and 'structure' in the 
American Heritage Dictionary and the Merriam Webster Dictionary.  In general, I 
have found the American Heritage definitions and etymologies very good.  They 
are usually clearer and more precise than the definitions in other 
dictionaries.  But it's always useful to get a second or third opinion.

An important distinction:  A structure is a pattern in an entity of some kind.  
A diagram is a pattern that somebody draws or imagines  as a representation or 
explanation of a pattern that somebody observed of found in some structure.

Therefore, a diagram would be more likely to be the kind of pattern that some 
human or animal or computer would be likely to use to support reasoning or 
computation about a pattern of any kind.

John

Definition of diagram

From American Heritage Dictionary:

  1. A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole.

  2. A graphic representation of an algebraic or geometric relationship.

  3. A chart or graph.

From Merriam Webster Dictionary:

  1. A graphic design that explains rather than represents; especially a drawing that shows arrangement and relations (as of parts).

  2. a line drawing made for mathematical or scientific purposes.

Definition of structure

From American Heritage Dictionary:

  1. Something made up of a number of parts that are held or put together in a particular way.

  2. The way in which parts are arranged or put together to form a whole; makeup.

  3. The interrelation or arrangement of parts in a complex entity.

From Merriam Webster Dictionary:

  1. The action of building; construction.

  2. Something (such as a building) that is constructed.

  3. Something arranged in a definite pattern of organization; leaves and other plant structures.

  4. Manner of construction; makeup.
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