Related papers: The Linking Probability of Deep Spider-Web Network…

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter…

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…

Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…

The probability distribution of the number $s$ of distinct sites visited up to time $t$ by a random walk on the fully-connected lattice with $N$ sites is first obtained by solving the eigenvalue problem associated with the discrete master…

Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three…

Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…

We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean…

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…

An $n$-tuple $D=(d(1),\dots,d(n))$ is a \emph{feasible degree sequence} if there is a graph on $\{1,\dots,n\}$ such that $i$ has degree $d(i)$. Any such graph will have $m=\sum_{i=1}^n d(i)/2$ edges. Letting $G(D)$ be a graph chosen…

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…

We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…

We consider qubit networks where adjacent qubits besides interacting via XY-coupling, also dissipate into the same environment. The steady states are computed exactly for all network sizes and topologies, showing that they are always…

The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…

We introduce a new method for predicting the formation of links in real-world networks, which we refer to as the method of effective transitions. This method relies on the theory of isospectral matrix reductions to compute the probability…

We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of Erd\H{o}s-R\'enyi networks of size $N$. These networks consist of vertices connected randomly with probability $p$…

The busy period for a queue is cast as the area swept under the random walk until it first returns to zero, $B$. Encompassing non-i.i.d. increments, the large-deviations asymptotics of $B$ is addressed, under the assumption that the…

We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…

It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta…

Let $Q^d$ be the $d$-dimensional binary hypercube. We say that $P=\{v_1,\ldots, v_k\}$ is an increasing path of length $k-1$ in $Q^d$, if for every $i\in [k-1]$ the edge $v_iv_{i+1}$ is obtained by switching some zero coordinate in $v_i$ to…