Related papers: On the construction of graph models realizing give…
The $K$-core of a graph is the unique maximum subgraph within which each vertex connects to $K$ or more other vertices. The optimal $K$-core attack problem asks to delete the minimum number of vertices from the $K$-core to induce its…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
Hypergraphs extend traditional networks by capturing multi-way or group interactions. Given the complexity of hypergraph data and the wide range of methodology available for pairwise network analysis, hypergraph data is often projected onto…
We study the query complexity of determining if a graph is connected with global queries. The first model we look at is matrix-vector multiplication queries to the adjacency matrix. Here, for an $n$-vertex graph with adjacency matrix $A$,…
Connectivity is a central notion of graph theory and plays an important role in graph algorithm design and applications. With emerging new applications in networks, a new type of graph connectivity problem has been getting more…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
This paper introduces a novel hypergraph classification algorithm. The use of hypergraphs in this framework has been widely studied. In previous work, hypergraph models are typically constructed using distance or attribute based methods.…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
Hypergraphs serve as a powerful tool for modeling complex relationships across domains like social networks, transactions, and recommendation systems. The (k,g)-core model effectively identifies cohesive subgraphs by assessing internal…
The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
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…
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…
In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…
The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It…
Four algorithms giving rise to graceful graphs from a known (non)graceful graph are described. Some necessary conditions for a graph to be highly graceful and critical are given. Finally some conjectures are made on graceful, critical and…