The small world of modular networks

@misc{citeulike:2477485, abstract = {A large number of networks occurring in reality exhibit modular structure. Such systems can be decomposed into distinct compartments whose members are highly inter-connected in comparison to the density of connections between compartments. Many of these networks also possess the small-world property, i.e., coexistence of high communication efficiency with strong local clustering among their elements. Although both these properties confer certain advantages to the corresponding network, especially in an evolutionary context, until now they have been considered to be independent features of the system. In this paper, we show through a simple model that the small-world property arises directly as a result of the modular configuration of such networks. The proposed network model, composed of sparsely connected modules, differs from previous models for small-world networks which typically assume connections to occur mostly among neighboring nodes on an underlying regular lattice with a few long-range links. We also establish a distinct dynamical signature for such modular networks, namely, the existence of two characteristic time scales in processes such as synchronization and diffusion, a significant difference from earlier small-world network models. This dichotomy between fast intra-modular dynamics and slow inter-modular dynamics is directly related to the topological structure of the model through the spectral behavior of the network Laplacian. By verifying the existence of similar features in the example of empirically determined cortico-cortical networks, we propose that the modular network model may better represent certain systems reported to have small-world properties.}, author = {Pan, Raj K. and Sinha, Sitabhra }, citeulike-article-id = {2477485}, eprint = {0802.3671}, keywords = {complex, dynamics, modular, networks, neural, structure}, month = {Feb}, posted-at = {2008-03-06 07:15:40}, priority = {2}, title = {The small world of modular networks}, url = {http://arxiv.org/abs/0802.3671}, year = {2008} }

TY - ELEC ID - citeulike:2477485 L3 - citeulike-article-id:2477485 N2 - A large number of networks occurring in reality exhibit modular structure. Such systems can be decomposed into distinct compartments whose members are highly inter-connected in comparison to the density of connections between compartments. Many of these networks also possess the small-world property, i.e., coexistence of high communication efficiency with strong local clustering among their elements. Although both these properties confer certain advantages to the corresponding network, especially in an evolutionary context, until now they have been considered to be independent features of the system. In this paper, we show through a simple model that the small-world property arises directly as a result of the modular configuration of such networks. The proposed network model, composed of sparsely connected modules, differs from previous models for small-world networks which typically assume connections to occur mostly among neighboring nodes on an underlying regular lattice with a few long-range links. We also establish a distinct dynamical signature for such modular networks, namely, the existence of two characteristic time scales in processes such as synchronization and diffusion, a significant difference from earlier small-world network models. This dichotomy between fast intra-modular dynamics and slow inter-modular dynamics is directly related to the topological structure of the model through the spectral behavior of the network Laplacian. By verifying the existence of similar features in the example of empirically determined cortico-cortical networks, we propose that the modular network model may better represent certain systems reported to have small-world properties. TI - The small world of modular networks KW - complex KW - dynamics KW - modular KW - networks KW - neural KW - structure AU - Pan, Raj AU - Sinha, Sitabhra PY - 2008/Feb/25/ UR - http://arxiv.org/abs/0802.3671 ER -