Abstract:
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.

Abstract:
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on identifying whether a topological hub, i.e. a node with high degree or strength, is also a dynamical hub, i.e. a node with high activity. We employ random walk dynamics and establish the necessary conditions for a network to be topologically and dynamically fully correlated, with topological hubs that are also highly active. Zipf's law is then shown to be a reflection of the match between structure and dynamics in a fully correlated network, as well as a consequence of the rich-get-richer evolution inherent in scale-free networks. We also examine a number of real networks for correlations between topology and dynamics and find that many of them are not fully correlated.

Abstract:
The study of network structure has uncovered organizational principles in complex systems. However, there is also a need to understand how to control them; for example, to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex multivariate systems can be predicted solely from the graph of interactions between variables, without considering variable dynamics: structural controllability and minimum dominating sets. Both methodologies utilize idealized assumptions about multivariate dynamics, yet most accurate models of real-world systems do not abide by these assumptions. Here, we study the relationship between network structure and the control of multivariate dynamics using three distinct measures of controllability in Boolean Networks. We demonstrate that structure-only methods fail to properly characterize controllability in these nonlinear systems; even in very simple networks, a large variation of possible dynamics can occur for the same structure, each with different control profiles. Our methodology is also used to characterize critical control variables in three models of biochemical regulation: the Drosophila melanogaster single-cell segment polarity network, the eukaryotic cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. Structure-only methods both undershoot and overshoot the number and which sets of variables actually control these models, highlighting the importance of the system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays a role in the extent to which structure predicts dynamics.

Abstract:
Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard deviations) of the time signals. While such approaches have led to many insights, they have failed to take into account that signals at different parts of the system can undergo distinct evolutions, which cannot be properly represented in terms of average values. A novel framework for identifying the principal aspects of the dynamics and how it is influenced by the network structure is proposed in this work. The potential of this approach is illustrated with respect to three important models (Integrate-and-Fire, SIS and Kuramoto), allowing the identification of highly structured dynamics, in the sense that different groups of nodes not only presented specific dynamics but also felt the structure of the network in different ways.

Abstract:
Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights based on regular network with initial homogeneous weight. The small world effect emerges due to the weight randomization. Its effects on the dynamical systems coupled by weighted networks are also investigated. Randomization of weight can increase the transition temperature in Ising model and enhance the ability of synchronization of chaotic systems dramatically.

Abstract:
Networks are widely used to represent interaction pattern among the components in complex systems. Structures of real networks from differ- ent domains may vary quite significantly. Since there is an interplay be- tween network architecture and dynamics, structure plays an important role in communication and information spreading on a network. Here we investigate the underlying undirected topology of different biological networks which support faster spreading of information and are better in communication. We analyze the good expansion property by using the spectral gap and communicability between nodes. Different epidemic models are also used to study the transmission of information in terms of disease spreading through individuals (nodes) in those networks. More- over, we explore the structural conformation and properties which may be responsible for better communication. Among all biological networks studied here, the undirected structure of neuronal networks not only pos- sesses the small-world property but the same is expressed remarkably to a higher degree than any randomly generated network which possesses the same degree sequence. A relatively high percentage of nodes, in neuronal networks, form a higher core in their structure. Our study shows that the underlying undirected topology in neuronal networks is significantly qualitatively different than the same from other biological networks and that they may have evolved in such a way that they inherit a (undirected) structure which is excellent and robust in communication.

Abstract:
It has been proposed that the history and evolution of scientific ideas may reflect certain aspects of the underlying socio-cognitive frameworks in which science itself is developing. Systematic analyses of the development of scientific knowledge may help us to construct models of the collective dynamics of science. Aiming at scientific rigor, these models should be built upon solid empirical evidence, analyzed with formal tools leading to ever-improving results that support the related conclusions. Along these lines we studied the dynamics and structure of the development of research in genomics as represented by the entire collection of genomics-related scientific papers contained in the PubMed database. The analyzed corpus consisted in more than 49,000 articles published in the years 1987 (first appeareance of the term Genomics) to 2011, categorized by means of the Medical Subheadings (MeSH) content-descriptors. Complex networks were built where two MeSH terms were connected if they are descriptors of the same article(s). The analysis of such networks revealed a complex structure and dynamics that to certain extent resembled small-world networks. The evolution of such networks in time reflected interesting phenomena in the historical development of genomic research, including what seems to be a phase-transition in a period marked by the completion of the first draft of the Human Genome Project. We also found that different disciplinary areas have different dynamic evolution patterns in their MeSH connectivity networks. In the case of areas related to science, changes in topology were somewhat fast while retaining a certain core-stucture, whereas in the humanities, the evolution was pretty slow and the structure resulted highly redundant and in the case of technology related issues, the evolution was very fast and the structure remained tree-like with almost no overlapping terms.

This paper explores traffic dynamics and performance ofcomplex networks. Complex networks of various structures are studied.We use node betweenness centrality, network polarization, and average path length to capture the structural characteristics of a network. Network throughput, delay, and packet lossare used asnetwork performance measures. We investigate how internal traffic, throughput,delay, and packet loss change as a function of packet generation rate, network structure, queue type, and queuing discipline through simulation. Three network states are classified. Further,our work reveals that the parameters chosen to reflect network structure, including node betweenness centrality, network polarization, and average path length, play important roles in different states of the underlying networks.

Abstract:
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations for their dynamics, is not always suitable. The graph theoretical models may serve as a rough but powerful tool in such cases. In this thesis, I first consider the network modeling for the representation of the biological systems. Both the topological and dynamical investigation tools are developed and applied to the various model networks. In particular, the attractor features' scaling with system size and distributions are explored for model networks. Moreover, the theoretical robustness expressions are discussed and computational studies are done for confirmation. The main biological research in this thesis is to investigate the transcriptional regulation of gene expression with synchronously and deterministically updated Boolean network models. I explore the attractor structure and the robustness of the known interaction network of the yeast, Saccharomyces Cerevisiae and compare with the model networks. Furthermore, I discuss a recent model claiming a possible root to the topology of the yeast's gene regulation network and investigate this model dynamically. The thesis also included another study which investigates a relation between folding kinetics with a new network representation, namely, the incompatibility network of a protein's native structure. I showed that the conventional topological aspects of these networks are not statistically correlated with the phi-values, for the limited data that is available.

Abstract:
Here we develop and implement a new Markov chain simulation algorithm to generate simple, connected random graphs that have a specified degree sequence and level of clustering, but are random in all other respects. The implementation of the algorithm (ClustRNet: Clustered Random Networks) provides the generation of random graphs optimized according to a local or global, and relative or absolute measure of clustering. We compare our algorithm to other similar methods and show that ours more successfully produces desired network characteristics.Finding appropriate null models is crucial in bioinformatics research, and is often difficult, particularly for biological networks. As we demonstrate, the networks generated by ClustRNet can serve as random controls when investigating the impacts of complex network features beyond the byproduct of degree and clustering in empirical networks.ClustRNet generates ensembles of graphs of specified edge structure and clustering. These graphs allow for systematic study of the impacts of connectivity and redundancies on network function and dynamics. This process is a key step in unraveling the functional consequences of the structural properties of empirical biological systems and uncovering the mechanisms that drive these systems.Over the last decade, network models have advanced our understanding of biology at all scales, from gene regulatory networks to metabolic cycles to global food webs [1-4]. They are also driving the forefront of sociology, information technology and many other disciplines [5-7]. Researchers often build network models from empirical data and then seek to characterize and explain non-trivial structural properties such as heavy-tail degree distributions, clustering, short average path lengths, degree correlations and community structure [1,6-12]. Many of these properties appear in diverse natural and man-made systems, and can fundamentally influence dynamical processes of and on these networks [13-19].Clusterin