The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J. K\"{o}rner in 1973. Although the notion of graph...
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number. First, we introduce an undirected graph on all possible...
graph complexity measuresstructural complexityMany research problems are extremely complex, making interdisciplinary knowledge a necessity; consequently cooperative work in mixed teams is a common and increasing research procedure. In this paper, we evaluated information-theoretic network measures on publication...
Problems on Matchings and Independent Sets of a Graph Let $G$ be a finite simple graph. For $X \\subset V(G)$, the difference of $X$, $d(X) := |X| - |N (X)|$ where $N(X)$ is the neighborhood of $X$ and $\\max \\, \\{d(X):X\\subset V(G)\\}$ is called ...
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prékopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HW...
Let $$\mathcal{H}$$ be a hypergraph with n vertices. Suppose that d1,d2,…,dn are degrees of the vertices of $$\mathcal{H}$$ . The t-th graph entropy
Finally, we apply the existing outlier detection methods on the embedding space to detect the anomaly. The abnormal climate event is detected as a graph in a certain time interval where the entropy is different from most other graphs, which is defined as follows....
A Bartoš,J Bobok,P Pyrih,S Roth,B Vejnar 摘要: We study continuous countably (strictly) monotone maps defined on a tame graph, i.e., a special Peano continuum for which the set containing branchpoints and endpoints has a countable closure. In our investigation we confine ourselves to...
The nodes in the graph represent the markables, and the weights on the edges are derived from the classification probabilities. They designed a graph partitioning algorithm to find the best clustering of the markables from the graph. Show moreView article Coreference resolution: A review of ...
GraphScope is a unified distributed graph computing platform that provides a one-stop environment for performing diverse graph operations on a cluster of computers through a user-friendly Python interface. GraphScope makes multi-staged processing of large-scale graph data on compute clusters simply by ...