  In this paper we penetrate and extend the notion of local constancy in
graphical models that has been introduced by Honorio et al. (2009). We propose
Neighborhood-Fused Lasso, a method for model selection in high-dimensional
graphical models, leveraging locality information. Our approach is based on an
extension of the idea of node-wise regression (Meinshausen-B\"{u}hlmann, 2006)
by adding a fusion penalty. We propose a fast numerical algorithm for our
approach, and provide theoretical and numerical evidence for the fact that our
methodology outperforms related approaches that are ignoring the locality
information. We further investigate the compatibility issues in our proposed
methodology and derive bound for the quadratic prediction error and
$l_1$-bounds on the estimated coefficients.
