Paper Info
Title
Hypercube Graph Representations and Fuzzy Measures of Graph Properties
Abstract
We describe a novel hypercube graph representation for labeled graphs with arbitrary edge weights in the interval [0, 1]. This representation admits graphical models for weighted adjacency matrices, which are useful in a number of real world applications wherein the strength of connections between graph nodes is important. It enables us to bring to bear a full arsenal of fuzzy set theoretic measures such as fuzzy subsethood, entropy, completeness, and mutual subsethood to the description of graphs. Our hypercube representation also provides a direct similarity metric between pairs of graphs, which is particularly useful for external comparisons among sets of graphs. The unitary complement of this similarity metric in turn provides a distance metric between two graphs, thus enabling us to perform vector processing operations on graphs, e.g., clustering, change detection, hypothesis testing as to the independence of two graphs, feature extraction for neural network and/or statistical classifiers, and antecedent specification for fuzzy mappings. We derive the probability mass function of this metric for two independent random graphs. The hypercube graph representation finds applications in problems where we are dealing with labeled graphs, e.g., computer networks, social networks, graphical information retrieval, and data fusion problems involving virtual networks of events. Of special interest are labeled graphs with fixed vertices whose edges and their corresponding weights vary over time, as well as graphs that evolve in time by the addition of new vertices and edges.
Year
DOI
Venue
2007
10.1109/TFUZZ.2006.890684
IEEE T. Fuzzy Systems
Keywords
DocType
Volume
fuzzy subsethood,graphical information retrieval,fuzzy mapping,hypercube graph representations,hypercube representation,direct similarity,fuzzy set theoretic,fuzzy measures,hypercube graph representation,graph properties,independent random graph,graph node,novel hypercube graph representation,arsenic,fuzzy sets,fuzzy systems,hypothesis test,feature extraction,neural networks,entropy,neural network,probability,social network,probability mass function,fuzzy system,cognitive science,distance metric,information retrieval,graph theory,fuzzy set theory,random graph,graphical models,graphical model,vectors,fuzzy set,change detection,data fusion,testing,computer network,hypercubes,graph representation
Journal
15
Issue
ISSN
Citations 
6
1063-6706
2
PageRank 
References 
Authors
0.66
4
2
Name
Order
Citations
PageRank
J. T. Rickard131.14
Ronald R. Yager2986206.03