Related papers: Correlations between thresholds and degrees: An an…
Threshold models of cascades in the social sciences and economics explain the spread of opinion and innovation due to social influence. In threshold cascade models, fads or innovations spread between agents as determined by their…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced in [M.E.J. Newman, Phys.…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a…
Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the…
Recent studies of attacks on complex networks suggest that small initial breakdowns can lead to global cascades of overload failures in communication, economic trading, and supply-transportation systems, considering the defense methods is…
Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to…
We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…
We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree…
The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either…
Relationships between individuals in a social network, genes in biological systems, and spins in magnetic systems often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. However, most studies of complex…
We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own…
Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold…
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold…