1,124 research outputs found
Graph ambiguity
In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved
Edge Clique Cover of Claw-free Graphs
The smallest number of cliques, covering all edges of a graph , is
called the (edge) clique cover number of and is denoted by . It
is an easy observation that for every line graph with vertices,
. G. Chen et al. [Discrete Math. 219 (2000), no. 1--3, 17--26;
MR1761707] extended this observation to all quasi-line graphs and questioned if
the same assertion holds for all claw-free graphs. In this paper, using the
celebrated structure theorem of claw-free graphs due to Chudnovsky and Seymour,
we give an affirmative answer to this question for all claw-free graphs with
independence number at least three. In particular, we prove that if is a
connected claw-free graph on vertices with , then and equality holds if and only if is either the graph of
icosahedron, or the complement of a graph on vertices called twister or
the power of the cycle , for .Comment: 74 pages, 4 figure
Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective
Neural-symbolic computing has now become the subject of interest of both
academic and industry research laboratories. Graph Neural Networks (GNN) have
been widely used in relational and symbolic domains, with widespread
application of GNNs in combinatorial optimization, constraint satisfaction,
relational reasoning and other scientific domains. The need for improved
explainability, interpretability and trust of AI systems in general demands
principled methodologies, as suggested by neural-symbolic computing. In this
paper, we review the state-of-the-art on the use of GNNs as a model of
neural-symbolic computing. This includes the application of GNNs in several
domains as well as its relationship to current developments in neural-symbolic
computing.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape
Conditional aggregation-based Choquet integral on discrete space
We derive computational formulas for the generalized Choquet integral based
on the novel survival function introduced by M. Boczek et al. [1]. We
demonstrate its usefulness on the Knapsack problem and the problem of
accommodation options. Moreover, we describe sufficient and necessary
conditions under which novel survival functions based on different parameters
coincide. This is closely related to the incomparability of input vectors
(alternatives) in decision-making processes
Stochastic Data Clustering
In 1961 Herbert Simon and Albert Ando published the theory behind the
long-term behavior of a dynamical system that can be described by a nearly
uncoupled matrix. Over the past fifty years this theory has been used in a
variety of contexts, including queueing theory, brain organization, and
ecology. In all these applications, the structure of the system is known and
the point of interest is the various stages the system passes through on its
way to some long-term equilibrium.
This paper looks at this problem from the other direction. That is, we
develop a technique for using the evolution of the system to tell us about its
initial structure, and we use this technique to develop a new algorithm for
data clustering.Comment: 23 page
First-order limits, an analytical perspective
In this paper we present a novel approach to graph (and structural) limits
based on model theory and analysis. The role of Stone and Gelfand dualities is
displayed prominently and leads to a general theory, which we believe is
naturally emerging. This approach covers all the particular examples of
structural convergence and it put the whole in new context. As an application,
it leads to new intermediate examples of structural convergence and to a "grand
conjecture" dealing with sparse graphs. We survey the recent developments
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