Related papers: Bratteli--Vershik models and graph covering models
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…
We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a…
We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…
This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
A Bratteli diagram is a type of graph in which the vertices are split into finite subsets occupying an infinite sequence of levels, starting with a bottom level and moving to successively higher levels along edges connecting consecutive…
Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of elementary transformations which we call foldings and…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…