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.

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 Erdős-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.Various natural and man-made systems have been modeled under the network theory framework. Different network models with distinct design principles have been proposed to better understand these real-world networks. The eigenvalue spectrum of these networks not only contain information about structural characteristics of underlying networks but also provide insight to dynamical behaviour and stability of corresponding complex systems. Depending on the structural characteristics of underlying model networks, the spectra of these networks exhibit specific features. All these ascertain that the spectra of networks can be used as a practical tool for classifying and understanding different real-world systems represented as networks. In this review, we first discussed the features which the different regions of spectra furnish, in case of the model networks. Further, we went on to discuss spectral characteristics of real-world networks, with particular emphasis on their extent of similarities and differences with the spectra of model networks.has elucidated the importance of interactions which has led to fundamental understanding of emergent phenomena in various complex systems and processes, for instance, cellular signalling, disease spread, scientific collaboration, transportation, WWW, power grid and so on [1,2]. Many of these networks appear to share certain nontrivial, similar patterns in connections between their elements. An understanding to the origins of these patterns and identifying and characterizing new ones is one of the main driving forces for research in complex networks. Apart from various investigations which focus on direct measurements of the structural properties of networks, there have been studies demonstrating that properties of networks or graphs could be well characterized by the spectrum of associated adjacency matrix [3]. The spectrum of a network is the set of eigenvalues of its adjacency matrix (A ij ) and is denoted as λ i , where i = 1, 2, . . . , N such that λ 1 > λ 2 ≥ λ 3 ≥ . . . ≥ λ N . For an undirected network, the adjacency matrix is symmetric and consequently has real eigenvalues. For a directed network, the adjacency matrix is asymmetric and has complex eigenvalues. Further, there can be networks having weighted connections, negative couplings, etc. Note that here we have restricted ourselves to symmet...

We analyze protein-protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics of random matrix theory. We demonstrate that spectral rigidity, which quantifies long range correlations in eigenvalues, for all protein-protein interaction networks follow random matrix prediction up to certain ranges indicating randomness in interactions. After this range, deviation from the universality evinces underlying structural features in network.the universality class of Gaussian orthogonal ensemble (GOE) [1,2,3,4]. Systematic investigations performed on model networks establish correlation between their structural properties and spectral properties inspected by RMT. This paper validates the access of a mathematical tool, RMT, to study protein-protein interaction (PPI) networks of different species, as model systems, under RMT framework. By interaction we mean that a protein may change conformation of another protein leading to a change in its affinity for different groups or may lead to addition or removal of a group in the molecule. The interaction is highly specific i.e. it can discriminate among thousands of different molecules in its environment and selectively interact with one or two [5].A network representation of PPI in addition to providing a better understanding of protein function, serves us with a powerful model of various functional pathways elucidating mechanics at cellular level [6,7,8]. Recently it has been realized that analysis of a network representation of such interactions, in comparison to pairwise analysis, provides a much better understanding of the processes occurring in biological systems [9,10,11,12,13].These studies indicate a strong correlation between the interaction networks and expression properties of the proteins having similar expression dynamics i.e. they tend to form clusters of either static or dynamic proteins [14,15]. Furthermore, analysis of PPI networks have contributed in various disease related biological studies, for instance study of human interaction data and Alzheimer's disease proteins has enriched our knowledge about its protein targets [16]. Some of the PPI network studies reveal that pathogens tend to interact with hub proteins and proteins that are central to many paths in the network [17].Analysis performed here involves construction of networks in such a way that any pair of proteins can achieve only two states i.e. either they are connected or not connected. We demonstrate that nearest neighbor spacing distribution (NNSD) of PPI networks of different species exhibit a similar statistical behavior of RMT, bringing them all under the same universality class. Furthermore, long range correlations in spectra display a wide range of behaviors. RMT and Networks -What is the connection?The random matrix approach regarded the Hamiltonian of a heavy nucleus (which is ...

In the recent years, the multilayer networks have increasingly been realized as a more realistic framework to understand emergent physical phenomena in complex real world systems. We analyze a massive time-varying social data drawn from the largest film industry of the world under multilayer network framework. The framework enables us to evaluate the versatility of actors, which turns out to be an intrinsic property of lead actors. Versatility in dimers suggests that working with different types of nodes are more beneficial than with similar ones. However, the triangles yield a different relation between type of co-actor and the success of lead nodes indicating the importance of higher order motifs in understanding the properties of the underlying system. Furthermore, despite the degree-degree correlations of entire networks being neutral, multilayering picks up different values of correlation indicating positive connotations like trust, in the recent years. Analysis of weak ties of the industry uncovers nodes from lower degree regime being important in linking Bollywood clusters. The framework and the tools used herein may be used for unraveling the complexity of other real world systems.

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.