Step 1: Understanding the concept.
The question refers to vegetative propagation and branching pattern where lateral branches develop with a single internodal length, forming a characteristic floating structure.
Step 2: Analysis of Nerium.
Nerium shows normal woody branching and does not exhibit specialized short internodal lateral branches. Hence, it is incorrect.
Step 3: Analysis of Oxalis.
Oxalis shows bulb formation and leaf modifications but not this type of branching pattern. Hence, it is incorrect.
Step 4: Analysis of Eichhornia.
Eichhornia (water hyacinth) shows stolon-like structures with nodes and short internodes, where lateral branches appear with a single internodal length. Hence, this is correct.
Step 5: Analysis of Dioscorea.
Dioscorea shows tuber formation and climbing habit but not this specific branching pattern. Hence, it is incorrect.
Step 6: Final conclusion.
Only Eichhornia matches the given characteristic, so it is the correct answer.
\[
\boxed{(3)}
\]