We propose representing a text corpus as a labeled directed graph, where nodes represent words and weighted edges represent the syntactic relations between them, as derived by dependency parsing. Given this graph, we adopt a graph-based similarity measure based on random walks to derive a similarity measure between words, and also use supervised learning to improve the derived similarity measur...

We consider the reflectionless transport of Manakov solitons in networks. The system is modelled terms on metric graphs subject to transparent boundary conditions at branching points. Simple constraints combining equivalent usual Kirchhoff vertex with are derived nonlinearity coefficients. Although method used for a star graph, an extension more complicated graph topologies easily possible.

We propose representing a text corpus as a labeled directed graph, where nodes represent words and weighted edges represent the syntactic relations between them, as derived by dependency parsing. Given this graph, we adopt a graph-based similarity measure based on random walks to derive a similarity measure between words, and also use supervised learning to improve the derived similarity measur...

Many problems can be cast as statistical inference on an attributed random graph. Our motivation is change detection in communication graphs. We prove that tests based on a fusion of graph-derived and content-derived metadata can be more powerful than those based on graph or content features alone. For some basic attributed random graphmodels, we derive fusion tests from the likelihood ratio. W...

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

In this paper, we present a novel semi-supervised learning framework based on `1 graph. The `1 graph is motivated by that each datum can be reconstructed by the sparse linear superposition of the training data. The sparse reconstruction coefficients, used to deduce the weights of the directed `1 graph, are derived by solving an `1 optimization problem on sparse representation. Different from co...

A graph with a semiregular group of automorphisms can be thought as the derived cover arising from voltage graph. Since its inception, theory graphs and their covers has been powerful tool used in study significant degree symmetry. We generalise this to that is not necessarily semiregular, we several well-known results classical broader setting.