Related papers: Node-Independent Spanning Trees in Gaussian Networ…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly…
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…
This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown…
Gaussian Process is a non-parametric prior which can be understood as a distribution on the function space intuitively. It is known that by introducing appropriate prior to the weights of the neural networks, Gaussian Process can be…
A spanning 2-forest separating vertices $u$ and $v$ of an undirected connected graph is a spanning forest with 2 components such that $u$ and $v$ are in distinct components. Aside from their combinatorial significance, spanning 2-forests…
This paper considers Gaussian relay networks where a source transmits a message to a sink terminal with the help of one or more relay nodes. The relays work in half-duplex mode, in the sense that they can not transmit and receive at the…
We find that transport on scale-free random networks depends strongly on degree-correlated network topologies whereas transport on Erd$\ddot{o}$s-R$\acute{e}$nyi networks is insensitive to the degree correlation. An approach for the tuning…
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to…
We consider a network of nodes distributed in physical space without physical links communicating through message broadcasting over specified distances. Typically, communication using smaller distances is desirable due to savings in energy…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
In this series, we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects such as undirected graphs, directed graphs, bidirected graphs, hypergraphs and finitary matroids.…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or…
Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…