Related papers: Adhesion-induced Discontinuous Transitions and Cla…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly…
We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents' opinions are fixed, they…
Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of…
We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
We describe the anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking. We obtain exact results for the size of the giant connected component and…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
If a system undergoing phase transitions exhibits some characteristics of both first and second order, it is said to be of 'mixed order' or to display the Thouless effect. Such a transition is present in a simple model of a dynamic social…
Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
In eukaryotic cells, mitochondria form networks that range from highly fused interconnected structures to fragmented populations of individual organelles that undergo transient interactions. These structures can be described as temporal…
Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
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…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…