1,117 research outputs found
From random walks to distances on unweighted graphs
Large unweighted directed graphs are commonly used to capture relations
between entities. A fundamental problem in the analysis of such networks is to
properly define the similarity or dissimilarity between any two vertices.
Despite the significance of this problem, statistical characterization of the
proposed metrics has been limited. We introduce and develop a class of
techniques for analyzing random walks on graphs using stochastic calculus.
Using these techniques we generalize results on the degeneracy of hitting times
and analyze a metric based on the Laplace transformed hitting time (LTHT). The
metric serves as a natural, provably well-behaved alternative to the expected
hitting time. We establish a general correspondence between hitting times of
the Brownian motion and analogous hitting times on the graph. We show that the
LTHT is consistent with respect to the underlying metric of a geometric graph,
preserves clustering tendency, and remains robust against random addition of
non-geometric edges. Tests on simulated and real-world data show that the LTHT
matches theoretical predictions and outperforms alternatives.Comment: To appear in NIPS 201
On the limiting behavior of parameter-dependent network centrality measures
We consider a broad class of walk-based, parameterized node centrality
measures for network analysis. These measures are expressed in terms of
functions of the adjacency matrix and generalize various well-known centrality
indices, including Katz and subgraph centrality. We show that the parameter can
be "tuned" to interpolate between degree and eigenvector centrality, which
appear as limiting cases. Our analysis helps explain certain correlations often
observed between the rankings obtained using different centrality measures, and
provides some guidance for the tuning of parameters. We also highlight the
roles played by the spectral gap of the adjacency matrix and by the number of
triangles in the network. Our analysis covers both undirected and directed
networks, including weighted ones. A brief discussion of PageRank is also
given.Comment: First 22 pages are the paper, pages 22-38 are the supplementary
material
Line Graphs of Weighted Networks for Overlapping Communities
In this paper, we develop the idea to partition the edges of a weighted graph
in order to uncover overlapping communities of its nodes. Our approach is based
on the construction of different types of weighted line graphs, i.e. graphs
whose nodes are the links of the original graph, that encapsulate differently
the relations between the edges. Weighted line graphs are argued to provide an
alternative, valuable representation of the system's topology, and are shown to
have important applications in community detection, as the usual node partition
of a line graph naturally leads to an edge partition of the original graph.
This identification allows us to use traditional partitioning methods in order
to address the long-standing problem of the detection of overlapping
communities. We apply it to the analysis of different social and geographical
networks.Comment: 8 Pages. New title and text revisions to emphasise differences from
earlier paper
- …