There is first order logic. In this logic, it is possible to define structures, where all points have a similar neighborhood.
Structures with only one binary relation are called graphs. Classes of graphs can be dense or not dense. If a graph class is dense, this means that first order logic formulae cannot be easily interpreted in this class.
Now, my thesis deals with first order logic interpretations, which make algorithmic interpretations of first order logic formulae easy in a dense graph class.