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The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
The scale free structure p(k)~k^{-gamma} of protein-protein interaction networks can be reproduced by a static physical model in simulation. We inspect the model theoretically, and find the key reason for the model to generate apparent…
Protein-protein interactions can be properly modeled as scale-free complex networks, while the lethality of proteins has been correlated with the node degrees, therefore defining a lethality-centrality rule. In this work we revisit this…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Proteins are an important class of biomolecules that serve as essential building blocks of the cells. Their three-dimensional structures are responsible for their functions. In this thesis we have investigated the protein structures using a…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the world-wide web. We first determine the degree distribution of a growing network in which…
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…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
The principles underlying protein folding remains one of Nature's puzzles with important practical consequences for Life. An approach that has gathered momentum since the late 1990's, looks at protein hetero-polymers and their folding…