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We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
How do inter-organizational networks emerge? Accounting for interdependence among ties while studying tie formation is one of the key challenges in this area of research. We address this challenge using an equilibrium framework where firms'…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network…
With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks arises…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the…
Dispersed colloidal particles within a suspension can aggregate and spontaneously self-organize into a robust, percolating structure known as a gel. These network-like structures are prevalent in nature and play a critical role in many…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…
We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…