Does topology of Internet nodes matter? Of course.
By using certain shapes and forms we can have different properties of information flow. Information flow can be quicker, arrive at destination with better probability (especially if we have alternate routes around hubs or switches which cannot be points of failure in information flow).
If we make certain shapes of node graphs, name (enumerate) nodes appropriately, then we can define unambiguous language of commands (moving and sending messages at precisely formed routes - which can be useful when some nodes or routes are damaged or in other situations).
Mathematical apparatus can be used to optimize forms and calculate how they can be reformed.. like in 3D animation (calculating shortest paths to changing shape and form). (Later i will show computational model in which it is true).
(For disambiguation: Think about shape as of geometrical shape, and about form as of something that gives properties. for example: shape of a Sphere in Space is also Form or Idea, or object of perception - even if only thoughts or mental images are perceived in Mind only).
See also: Reforming Shapes, Factorization Tree, Formation of sixty, eighty four.