4,272 research outputs found
VoG: Summarizing and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple
sentences? How can we measure the "importance" of a set of discovered subgraphs
in a large graph? These are exactly the problems we focus on. Our main ideas
are to construct a "vocabulary" of subgraph-types that often occur in real
graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the
most succinct description of a graph in terms of this vocabulary. We measure
success in a well-founded way by means of the Minimum Description Length (MDL)
principle: a subgraph is included in the summary if it decreases the total
description length of the graph.
Our contributions are three-fold: (a) formulation: we provide a principled
encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop
\method, an efficient method to minimize the description cost, and (c)
applicability: we report experimental results on multi-million-edge real
graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201
{VoG}: {Summarizing} and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph
Decomposition theorem on matchable distributive lattices
A distributive lattice structure has been established on the
set of perfect matchings of a plane bipartite graph . We call a lattice {\em
matchable distributive lattice} (simply MDL) if it is isomorphic to such a
distributive lattice. It is natural to ask which lattices are MDLs. We show
that if a plane bipartite graph is elementary, then is
irreducible. Based on this result, a decomposition theorem on MDLs is obtained:
a finite distributive lattice is an MDL if and only if each factor
in any cartesian product decomposition of is an MDL. Two types of
MDLs are presented: and , where
denotes the cartesian product between -element
chain and -element chain, and is a poset implied by any
orientation of a tree.Comment: 19 pages, 7 figure
- …