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It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
We address the problem of social network de-anonymization when relationships between people are described by scale-free graphs. In particular, we propose a rigorous, asymptotic mathematical analysis of the network de-anonymization problem…
In this paper, we study through mathematical modelling the combined effect of transcriptional and translational regulation by proteins and small noncoding RNAs (sRNA) in a genetic feedback motif that has an important role in the survival of…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
It has been estimated that about 30% of the genes in the human genome are regulated by microRNAs (miRNAs). These are short RNA sequences that can down-regulate the levels of mRNAs or proteins in animals and plants. Genes regulated by miRNAs…
We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a…
We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…
In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RAN) as they can be considered…
We propose and study a model of traffic in communication networks. The underlying network has a structure that is tunable between a scale-free growing network with preferential attachments and a random growing network. To model realistic…
We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for…
Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free…
We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-\gamma}$. In particular, we focus on finite-size trees in a…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
We study counter expressed gene networks constructed from gene-expression data obtained from many types of cancers. The networks are synthesized by connecting vertices belonging to each others' list of K-farthest-neighbors, with K being an…