Related papers: Critical phenomena in heterogeneous k-core percola…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate…
We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erd\H{o}s--R\'enyi graph to a $2D$ lattice at the characteristic interaction…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Complex networks with high numbers of nodes or links are often difficult to analyse. However, not all elements contribute equally to their structural patterns. A small number of elements (the hubs) seem to play a particularly relevant role…
A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how…
Neural networks with equal excitatory and inhibitory feedback show high computational performance. They operate close to a critical point characterized by the joint activation of large populations of neurons. Yet, in macaque motor cortex we…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…