Comparative statistical study of two local clustering coefficient formulations as tropical cyclone markers for climate networks

We introduce a new formulation of local clustering coefficient for weighted correlation networks. This new formulation is based upon a definition introduced previously in the neuroscience context and aimed at compensating for spurious correlations caused by indirect interactions. We modify this definition further by replacing Pearson's pairwise correlation coefficients and three-way partial correlation coefficients by the respective Kendall's rank correlations. This reduces statistical sample size requirements to compute the correlations, which translates into the possibility of using shorter time windows and hence into a shorter response time of the real-time climate network analysis. We construct evolving climate networks of mean sea level pressure fluctuations and analyze anomalies of local clustering coefficient in these networks. We develop a broadly applicable statistical methodology to study association between spatially inhomogeneous georeferenced multivariate time series and binary-valued spatiotemporal data (or other data reducible to this representation) and use it to compare the newly proposed formulation of local clustering coefficient (for weighted correlation networks) to the conventional one (for unweighted graphs) in terms of the association of these measures in climate networks to tropical cyclones. Thus we substantiate the previously made observation that tropical cyclones are associated with anomalously high values of local clustering coefficient, and confirm that the new formulation shows a stronger association

Configuration model for correlation matrices preserving the node strength

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analysed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.Comment: 8 figures, 4 table

Assortative mixing in Protein Contact Networks and protein folding kinetics

Starting from linear chains of amino acids, the spontaneous folding of proteins into their elaborate three-dimensional structures is one of the remarkable examples of biological self-organization. We investigated native state structures of 30 single-domain, two-state proteins, from complex networks perspective, to understand the role of topological parameters in proteins' folding kinetics, at two length scales-- as ``Protein Contact Networks (PCNs)'' and their corresponding ``Long-range Interaction Networks (LINs)'' constructed by ignoring the short-range interactions. Our results show that, both PCNs and LINs exhibit the exceptional topological property of ``assortative mixing'' that is absent in all other biological and technological networks studied so far. We show that the degree distribution of these contact networks is partly responsible for the observed assortativity. The coefficient of assortativity also shows a positive correlation with the rate of protein folding at both short and long contact scale, whereas, the clustering coefficients of only the LINs exhibit a negative correlation. The results indicate that the general topological parameters of these naturally-evolved protein networks can effectively represent the structural and functional properties required for fast information transfer among the residues facilitating biochemical/kinetic functions, such as, allostery, stability, and the rate of folding.Comment: Published in Bioinformatic

Network Analysis of Intrinsic Functional Brain Connectivity in Alzheimer's Disease

Functional brain networks detected in task-free (“resting-state”) functional magnetic resonance imaging (fMRI) have a small-world architecture that reflects a robust functional organization of the brain. Here, we examined whether this functional organization is disrupted in Alzheimer's disease (AD). Task-free fMRI data from 21 AD subjects and 18 age-matched controls were obtained. Wavelet analysis was applied to the fMRI data to compute frequency-dependent correlation matrices. Correlation matrices were thresholded to create 90-node undirected-graphs of functional brain networks. Small-world metrics (characteristic path length and clustering coefficient) were computed using graph analytical methods. In the low frequency interval 0.01 to 0.05 Hz, functional brain networks in controls showed small-world organization of brain activity, characterized by a high clustering coefficient and a low characteristic path length. In contrast, functional brain networks in AD showed loss of small-world properties, characterized by a significantly lower clustering coefficient (p<0.01), indicative of disrupted local connectivity. Clustering coefficients for the left and right hippocampus were significantly lower (p<0.01) in the AD group compared to the control group. Furthermore, the clustering coefficient distinguished AD participants from the controls with a sensitivity of 72% and specificity of 78%. Our study provides new evidence that there is disrupted organization of functional brain networks in AD. Small-world metrics can characterize the functional organization of the brain in AD, and our findings further suggest that these network measures may be useful as an imaging-based biomarker to distinguish AD from healthy aging

Statistical Self-Similar Properties of Complex Networks

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability depends on the type of networks. To unravel ubiquitous characteristics that complex networks may have in common, we adopt the clustering coefficient as the probability measure, and present a systematic analysis of various types of complex networks from the perspective of statistical self-similarity. We find that the probability distribution of the clustering coefficient is best characterized by the multifractal; moreover, the support of the measure had a fractal dimension. These two features enable us to describe complex networks in a unified way; at the same time, offer unforeseen possibilities to comprehend complex networks.Comment: 11 pages, 4 figure