Related papers: Nonstandard Digraphs
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
Over the last few years, network science has proved to be useful in modeling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex…
Nonlinear supersymmetry is characterized by supercharges to be higher order in bosonic momenta of a system, and thus has a nature of a hidden symmetry. We review some aspects of nonlinear supersymmetry and related to it exotic supersymmetry…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…
Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave…
Real-world graphs are complex to process for performing effective analysis, such as anomaly detection. However, recently, there have been several research efforts addressing the issues surrounding graph-based anomaly detection. In this…
In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced\-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs -- these range from sets of social groups, events, or collaboration projects to the vast collection of…
Most previous work on neural text generation from graph-structured data relies on standard sequence-to-sequence methods. These approaches linearise the input graph to be fed to a recurrent neural network. In this paper, we propose an…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
The transmission of a connected hypergraph is defined as the summation of distances between all unordered pairs of distinct vertices. We determine the unique uniform unicyclic hypergraphs of fixed size with minimum and maximum…
Diffusion has shown great success in improving accuracy of unsupervised image retrieval systems by utilizing high-order structures of image manifold. However, existing diffusion methods suffer from three major limitations: 1) they usually…
To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed…
In this paper, we propose two novel approaches for hypergraph comparison. The first approach transforms the hypergraph into a graph representation for use of standard graph dissimilarity measures. The second approach exploits the…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…