It is widely accepted that biological hierarchy can be well characterized by a "deterministic hierarchical model", because it reconciles modularity and scale-freeness, with C(k) following a scaling law [ 7].
Metabolomic correlation approaches have highlighted some properties (e.g. modularity and scale-freeness) in several species including plants [ 13- 16].
It has been claimed that many of the properties exhibited by metabolic networks such as modularity and scale-free degree distributions are products of adaptive evolution.
The coexistence of modularity and a scale-free degree distribution can be explained by assuming a hierarchical modular network organization [ 43, 47, 49].
However, in protein families, modularity, local clustering and scale-free topology coexist [ 19].
In protein similarity graphs, modularity, local clustering and scale-free topology [ 19] coexist.
In object-oriented programming (OOP) languages, the ability to encapsulate software concerns of the dominant decomposition in objects is the key to reaching high modularity and loss of complexity in large scale designs.
This observation may be related to a recent finding that, in a complex network, the large-scale topological organization (characterized by the degree exponents of the scale-free and hierarchical modularity) and the variable counts of the different motif topologies can define each other [ 28, 29].
This principle is used together with modularity and hierarchy to guide the design of large-scale complex software systems.
The analysis reveals that clustering, modularity and long path lengths all play an important part in the design of robust large-scale infrastructure.
Modularity and gradients may thus coexist, and complement one another.
