Related papers: Cumulative Merging Percolation: A long-range perco…
There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…
The amount of available data about complex systems is increasing every year, measurements of larger and larger systems are collected and recorded. A natural representation of such data is given by networks, whose size is following the size…
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…
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…
We introduce a new kind of percolation on finite graphs called jigsaw percolation. This model attempts to capture networks of people who innovate by merging ideas and who solve problems by piecing together solutions. Each person in a social…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
The Message-Passing Approach (MPA) is the state-of-the-art technique to obtain quasi-analytical predictions for percolation on real complex networks. Besides being intuitive and straightforward, it has the advantage of being mathematically…
We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
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…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…