Generalized hierarchical completely-connected networks

A novel network structure called generalized Hierarchical Completely-Connected networks (HCC) is proposed, and its properties and features are evaluated. A set of the HCCs constructed by the proposed method includes some conventional hierarchical networks (then it is called generalized). The construction of an HCC is started from a basic block (a level-1 block) which consists of n nodes with a constant degree. Then a level-h (h⩾2) block is constructed recursively by interconnecting any pair of macro nodes (n level-(h-1) blocks) completely. An HCC has the constant node degree regardless of increasing its size (the number of nodes). Furthermore, since an HCC has a hierarchically structured character and the feature of uniformity, a wide variety of inter-cluster connections are possible