Concise Fuzzy Representation of Big Graphs: a Dimensionality Reduction
  Approach
  The enormous amount of data to be represented using large graphs exceeds in
some cases the resources of a conventional computer. Edges in particular can
take up a considerable amount of memory as compared to the number of nodes.
However, rigorous edge storage might not always be essential to be able to draw
the needed conclusions. A similar problem takes records with many variables and
attempts to extract the most discernible features. It is said that the
"dimension" of this data is reduced. Following an approach with the same
objective in mind, we can map a graph representation to a k-dimensional space
and answer queries of neighboring nodes by measuring Euclidean distances. The
accuracy of our answers would decrease but would be compensated for by fuzzy
logic which gives an idea about the likelihood of error. This method allows for
reasonable representation in memory while maintaining a fair amount of useful
information. Promising preliminary results are obtained and reported by testing
the proposed approach on a number of Facebook graphs.
