Coarse-Graining Method Based on Hierarchical Clustering on Complex Networks

Entrograms and coarse graining of dynamics on complex networks

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov process according to a partition impacts on the thus obtained lower-dimensional dynamics. We highlight that for a dynamics on a particular graph there may be multi...

Geographical coarse graining of complex networks.

We perform a renormalization-grouplike numerical analysis of geographically embedded complex networks on a two-dimensional square lattice. At each step of the coarse-graining procedure, the four vertices on each 2x2 square box are merged to a single vertex, resulting in a coarse-grained system of smaller size. Repetition of the process leads to the observation that the coarse-graining procedure...

Spectral coarse graining of complex networks.

Reducing the complexity of large systems described as complex networks is key to understanding them and a crucial issue is to know which properties of the initial system are preserved in the reduced one. Here we use random walks to design a coarse graining scheme for complex networks. By construction the coarse graining preserves the slow modes of the walk, while reducing significantly the size...

Simplifying Complex networkS: from a CluStering to a CoarSe graining Strategy

The framework of complex networks has been shown to describe adequately a wide class of complex systems made up of a large number of interacting units. In this framework, a node is associated to each unit and two nodes are connected by an edge if the two units interact with each other. Examples of such systems can be found in living organisms—the map of interactions between proteins or the netw...

Shape-Based Coarse Graining