Spectral properties of complex networks.

This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part of the spectrum, and (c) degenerate eigenvalues, based on the intrinsic properties of eigenvalues and the phenomena they capture. We have reviewed the works done for spectra of various popular model networks, such as the Erdos-Rényi random networks, scale-free networks, 1-d lattice, small-world networks, and various different real-world networks. Additionally, potential applications of spectral properties for natural processes have been reviewed.

Codon based co-occurrence network motifs in human mitochondria.

The nucleotide polymorphism in the human mitochondrial genome (mtDNA) tolled by codon position bias plays an indispensable role in human population dispersion and expansion. Herein, genome-wide nucleotide co-occurrence networks were constructed using data comprised of five different geographical regions and around 3000 samples for each region. We developed a powerful network model to describe complex mitochondrial evolutionary patterns among codon and non-codon positions. We found evidence that the evolution of human mitochondria DNA is dominated by adaptive forces, particularly mutation and selection, which was supported by many previous studies. The diversity observed in the mtDNA was compared with mutations, co-occurring mutations, network motifs considering codon positions as causing agent. This comparison showed that long-range nucleotide co-occurrences have a large effect on genomic diversity. Most notably, codon motifs apparently underpinned the preferences among codon positions for co-evolution which is probably highly biased during the origin of the genetic code. Our analysis also showed that variable nucleotide positions of different human sub-populations implemented the independent mtDNA evolution to its geographical dispensation. Ergo, this study has provided both a network framework and a codon glance to investigate co-occurring genomic variations that are critical in underlying complex mitochondrial evolution.

Uncovering randomness and success in society.

An understanding of how individuals shape and impact the evolution of society is vastly limited due to the unavailability of large-scale reliable datasets that can simultaneously capture information regarding individual movements and social interactions. We believe that the popular Indian film industry, "Bollywood", can provide a social network apt for such a study. Bollywood provides massive amounts of real, unbiased data that spans more than 100 years, and hence this network has been used as a model for the present paper. The nodes which maintain a moderate degree or widely cooperate with the other nodes of the network tend to be more fit (measured as the success of the node in the industry) in comparison to the other nodes. The analysis carried forth in the current work, using a conjoined framework of complex network theory and random matrix theory, aims to quantify the elements that determine the fitness of an individual node and the factors that contribute to the robustness of a network. The authors of this paper believe that the method of study used in the current paper can be extended to study various other industries and organizations.