Modularity and anti-modularity in networks with arbitrary degree distribution

Partitioning and modularity of graphs with arbitrary degree distribution.

We solve the graph bipartitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut size to scale universally with . In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with square root [Fu and Anderson, J. Phys. A 19, 1605 (1986)]. Our results also generalize...

Networks, dynamics, and modularity.

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymp...

Modularity of Ontologies in an Arbitrary Institution

The notion of module extraction has been studied extensively in the ontology community. The idea is to extract, from a large ontology, those axioms that are relevant to certain concepts of interest (formalised as a subsignature). The technical concept used for the definition of module extraction is that of inseparability, which is related to indistinguishability known from observational specifi...

Modularity within Neural Networks

Open Regulatory Networks and Modularity

We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is put on the interplay between the internal properties of the open systems and the different possible inputs on them to deduce new functionalities of the modules...