Related papers: Percolation on bipartite scale-free networks
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
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…
Large-scale power blackouts caused by cascading failure are inflicting enormous socioeconomic costs. We study the problem of cascading link failures in power networks modelled by random geometric graphs from a percolation-based viewpoint.…
In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $\alpha$ and…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
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…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
The studies based on $A+A \rightarrow \emptyset$ and $A+B\rightarrow \emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports,…
Understanding what types of phenomena lead to discontinuous phase transitions in the connectivity of random networks is an outstanding challenge. Here we show that a simple stochastic model of graph evolution leads to a discontinuous…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic…
We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network. Using the renormalization-group like procedure, we derive the recursion relations for the percolating…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…