Communicability Angle and the Spatial Efficiency of Networks

We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of the edges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.Comment: Revised. 27 pages, 14 figure

Beware of the Small-World neuroscientist!

The SW has undeniably been one of the most popular network descriptors in the neuroscience literature. Two main reasons for its lasting popularity are its apparent ease of computation and the intuitions it is thought to provide on how networked systems operate. Over the last few years, some pitfalls of the SW construct and, more generally, of network summary measures, have widely been acknowledged

Communicability distance reveals hidden patterns of alzheimer’s disease

The communicability distance between pairs of regions in human brain is used as a quantitative proxy for studying Alzheimer’s disease. Using this distance, we obtain the shortest communicability path lengths between different regions of brain networks from patients with Alzheimer’s disease (AD) and healthy cohorts (HC). We show that the shortest communicability path length is significantly better than the shortest topological path length in distinguishing AD patients from HC. Based on this approach, we identify 399 pairs of brain regions for which there are very significant changes in the shortest communicability path length after AD appears. We find that 42% of these regions interconnect both brain hemispheres, 28% connect regions inside the left hemisphere only, and 20% affect vermis connection with brain hemispheres. These findings clearly agree with the disconnection syndrome hypothesis of AD. Finally, we show that in 76.9% of damaged brain regions the shortest communicability path length drops in AD in relation to HC. This counterintuitive finding indicates that AD transforms the brain network into a more efficient system from the perspective of the transmission of the disease, because it drops the circulability of the disease factor around the brain regions in relation to its transmissibility to other regions