Related papers: Continuum Percolation in the Intrinsically Secure …
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_n$. Given an initial set $G\subseteq K_n$ of infected edges, the transmission of the virus is governed by a fixed graph $H$: in each…
We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast to previous studies on the SINR graphs, we consider both a…
Intelligent reflecting surfaces (IRSs) have several prominent advantages, including improving the level of wireless communication security and privacy. In this work, we focus on the latter aspect and introduce a strategy to counteract the…
Integrated sensing and communication (ISAC) is a cornerstone technology for 6G networks, offering unified support for high-rate communication and high-accuracy sensing. While existing literature extensively covers link-level designs, the…
We study the phenomenon of information propagation on mobile geometric scale-free random graphs, where vertices instantaneously pass on information to all other vertices in the same connected component. The graphs we consider are…
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 functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
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…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
Publishing graph data is widely desired to enable a variety of structural analyses and downstream tasks. However, it also potentially poses severe privacy leakage, as attackers may leverage the released graph data to launch attacks and…
The advancement in wireless communication technologies is becoming more demanding and pervasive. One of the fundamental parameters that limit the efficiency of the network are the security challenges. The communication network is vulnerable…
We propose the notion of {\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$,…
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function…
We study the SIR ("susceptible, infected, removed/recovered") model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally,…
We define an inhomogeneous percolation model on "ladder graphs" obtained as direct products of an arbitrary graph $G = (V,E)$ and the set of integers $\mathbb{Z}$ (vertices are thought of as having a "vertical" component indexed by an…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Long range flight by fixed-wing aircraft without propulsion systems can be accomplished by "soaring" -- exploiting randomly located updrafts to gain altitude which is expended in gliding flight. As the location of updrafts is uncertain and…