  Recent studies uncovered important core/periphery network structures
characterizing complex sets of cooperative and competitive interactions between
network nodes, be they proteins, cells, species or humans. Better
characterization of the structure, dynamics and function of core/periphery
networks is a key step of our understanding cellular functions, species
adaptation, social and market changes. Here we summarize the current knowledge
of the structure and dynamics of "traditional" core/periphery networks,
rich-clubs, nested, bow-tie and onion networks. Comparing core/periphery
structures with network modules, we discriminate between global and local
cores. The core/periphery network organization lies in the middle of several
extreme properties, such as random/condensed structures, clique/star
configurations, network symmetry/asymmetry, network
assortativity/disassortativity, as well as network hierarchy/anti-hierarchy.
These properties of high complexity together with the large degeneracy of core
pathways ensuring cooperation and providing multiple options of network flow
re-channelling greatly contribute to the high robustness of complex systems.
Core processes enable a coordinated response to various stimuli, decrease
noise, and evolve slowly. The integrative function of network cores is an
important step in the development of a large variety of complex organisms and
organizations. In addition to these important features and several decades of
research interest, studies on core/periphery networks still have a number of
unexplored areas.
