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deepstruct connects deep learning models and graph theory such that different graph structures can be imposed on neural networks or graph structures can be extracted from trained neural network models. For this, deepstruct provides deep…
The graph entropy describes the structural information of graph. Motivated by the definition of graph entropy in general graphs, the graph entropy of hypergraphs based on Laplacian degree are defined. Some results on graph entropy of simple…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the…
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper,…
We describe triples and systems, expounded as an axiomatic algebraic umbrella theory for classical algebra, tropical algebra, hyperfields, and fuzzy rings.
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
This paper introduces the recent work of Nebula Graph, an open-source, distributed, scalable, and native graph database. We present a system design trade-off and a comprehensive overview of Nebula Graph internals, including graph data…
An Euler tour of a hypergraph is a closed walk that traverses every edge exactly once; if a hypergraph admits such a walk, then it is called eulerian. Although this notion is one of the progenitors of graph theory --- dating back to the…
Recent advancements of complex network representation among several disciplines motivated the investigation of exoplanetary dynamics by means of recurrence networks. We are able to recover different dynamical regimes by means of various…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\times Set$ and use the…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…