1 research outputs found
Lossless Representation of Graphs using Distributions
We consider complete graphs with edge weights and/or node weights taking
values in some set. In the first part of this paper, we show that a large
number of graphs are completely determined, up to isomorphism, by the
distribution of their sub-triangles. In the second part, we propose graph
representations in terms of one-dimensional distributions (e.g., distribution
of the node weights, sum of adjacent weights, etc.). For the case when the
weights of the graph are real-valued vectors, we show that all graphs, except
for a set of measure zero, are uniquely determined, up to isomorphism, from
these distributions. The motivating application for this paper is the problem
of browsing through large sets of graphs.Comment: 19 page