7,182 research outputs found
Relations Between Adjacency and Modularity Graph Partitioning
In this paper the exact linear relation between the leading eigenvector of
the unnormalized modularity matrix and the eigenvectors of the adjacency matrix
is developed. Based on this analysis a method to approximate the leading
eigenvector of the modularity matrix is given, and the relative error of the
approximation is derived. A complete proof of the equivalence between
normalized modularity clustering and normalized adjacency clustering is also
given. Some applications and experiments are given to illustrate and
corroborate the points that are made in the theoretical development.Comment: 11 page
Stochastic Block Transition Models for Dynamic Networks
There has been great interest in recent years on statistical models for
dynamic networks. In this paper, I propose a stochastic block transition model
(SBTM) for dynamic networks that is inspired by the well-known stochastic block
model (SBM) for static networks and previous dynamic extensions of the SBM.
Unlike most existing dynamic network models, it does not make a hidden Markov
assumption on the edge-level dynamics, allowing the presence or absence of
edges to directly influence future edge probabilities while retaining the
interpretability of the SBM. I derive an approximate inference procedure for
the SBTM and demonstrate that it is significantly better at reproducing
durations of edges in real social network data.Comment: To appear in proceedings of AISTATS 201
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