Comparative evaluation of community-aware centrality measures

Krabbe disease (KD) is a neurodegenerative disorder caused by the lack of β- galactosylceramidase enzymatic activity and by widespread accumulation of the cytotoxic galactosyl-sphingosine in neuronal, myelinating and endothelial cells. Despite the wide use of Twitcher mice as experimental model for KD, the ultrastructure of this model is partial and mainly addressing peripheral nerves. More details are requested to elucidate the basis of the motor defects, which are the first to appear during KD onset. Here we use transmission electron microscopy (TEM) to focus on the alterations produced by KD in the lower motor system at postnatal day 15 (P15), a nearly asymptomatic stage, and in the juvenile P30 mouse. We find mild effects on motorneuron soma, severe ones on sciatic nerves and very severe effects on nerve terminals and neuromuscular junctions at P30, with peripheral damage being already detectable at P15. Finally, we find that the gastrocnemius muscle undergoes atrophy and structural changes that are independent of denervation at P15. Our data further characterize the ultrastructural analysis of the KD mouse model, and support recent theories of a dying-back mechanism for neuronal degeneration, which is independent of demyelination.

Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as "modularity" over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known--a collaboration network and a food web--and find that it detects significant and informative community divisions in both cases.