3,424 research outputs found
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
Applications of Structural Balance in Signed Social Networks
We present measures, models and link prediction algorithms based on the
structural balance in signed social networks. Certain social networks contain,
in addition to the usual 'friend' links, 'enemy' links. These networks are
called signed social networks. A classical and major concept for signed social
networks is that of structural balance, i.e., the tendency of triangles to be
'balanced' towards including an even number of negative edges, such as
friend-friend-friend and friend-enemy-enemy triangles. In this article, we
introduce several new signed network analysis methods that exploit structural
balance for measuring partial balance, for finding communities of people based
on balance, for drawing signed social networks, and for solving the problem of
link prediction. Notably, the introduced methods are based on the signed graph
Laplacian and on the concept of signed resistance distances. We evaluate our
methods on a collection of four signed social network datasets.Comment: 37 page
The normalized Laplacian spectrum of subdivisions of a graph
Determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated subdivisions of simple connected graphs. As an example of application of these results we find the exact values of their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.Postprint (published version
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