4 research outputs found
Towards Quantifying Vertex Similarity in Networks
Vertex similarity is a major problem in network science with a wide range of
applications. In this work we provide novel perspectives on finding
(dis)similar vertices within a network and across two networks with the same
number of vertices (graph matching). With respect to the former problem, we
propose to optimize a geometric objective which allows us to express each
vertex uniquely as a convex combination of a few extreme types of vertices. Our
method has the important advantage of supporting efficiently several types of
queries such as "which other vertices are most similar to this vertex?" by the
use of the appropriate data structures and of mining interesting patterns in
the network. With respect to the latter problem (graph matching), we propose
the generalized condition number --a quantity widely used in numerical
analysis-- of the Laplacian matrix representations of
as a measure of graph similarity, where are the graphs of interest. We
show that this objective has a solid theoretical basis and propose a
deterministic and a randomized graph alignment algorithm. We evaluate our
algorithms on both synthetic and real data. We observe that our proposed
methods achieve high-quality results and provide us with significant insights
into the network structure.Comment: 16 papers, 5 figures, 2 table
Annual Research Report, 2009-2010
Annual report of collaborative research projects of Old Dominion University faculty and students in partnership with business, industry and governmenthttps://digitalcommons.odu.edu/or_researchreports/1001/thumbnail.jp