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Emphasis Selection is a newly proposed task which focuses on choosing words for emphasis in short sentences. Traditional methods only consider the sequence information of a sentence while ignoring the rich sentence structure and word…
An incidence in a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ is an edge of $G$ incident to $v$. Two incidences $(v,e)$ and $(u,f)$ are adjacent if at least one of the following holds: $(a)$ $v = u$, $(b)$ $e = f$, or…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of…
Graph traversals are a basic but fundamental ingredient for a variety of graph algorithms and graph-oriented queries. To achieve the best possible query performance, they need to be implemented at the core of a database management system…
Causal discovery aims to recover information about an unobserved causal graph from the observable data it generates. Layerings are orderings of the variables which place causes before effects. In this paper, we provide ways to recover…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…
The adjacency-diametrical matrix (AD matrix) of a connected graph $G$ with diameter $d$, denoted by $AD(G)$, is the matrix indexed by the vertices of $G$ in which the $(i,j)$-entry of $AD(G)$ is $1$ if $d_G(v_i,v_j)=1$, is $d$ if…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
A real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. However, most existing methods lack consideration of the intrinsic differences in relations between nodes caused…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we…
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…
To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…
The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them…