Related papers: Robustness of Interdependent Random Geometric Netw…
We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a…
Integrative analysis of multi-level pharmacogenomic data for modeling dependencies across various biological domains is crucial for developing genomic-testing based treatments. Chain graphs characterize conditional dependence structures of…
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is…
We study the mixing time of random graphs in the $d$-dimensional toric unit cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a…
Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of the two canonical assumptions: (i) a homogeneous graph with a common network…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
We provide sufficient conditions for a regular graph $G$ of growing degree $d$, guaranteeing a phase transition in its random subgraph $G_p$ similar to that of $G(n,p)$ when $p\cdot d\approx 1$. These conditions capture several well-studied…
Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…
In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…
Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it…
Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak…
Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph…
We study the giant component problem slightly above the critical regime for percolation on Poissonian random graphs in the scale-free regime, where the vertex weights and degrees have a diverging second moment. Critical percolation on…