Related papers: Superport networks
Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical…
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
For successful estimation, the usual network tomography algorithms crucially require i) end-to-end data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations…
An unexpected and somewhat surprising observation is that two counter-cascaded systems, given the right conditions, can exhibit multivaluedness from one of the outputs to the other. The main result presented here is a necessary and…
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…
The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…
We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by…
Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E…
The key technologies of sixth generation (6G), such as ultra-massive multiple-input multiple-output (MIMO), enable intricate interactions between antennas and wireless propagation environments. As a result, it becomes necessary to develop…
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…
In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…