The Stanford GraphBase: a platform for combinatorial computing
The Stanford GraphBase: a platform for combinatorial computing
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A mathematical theory of communication
ACM SIGMOBILE Mobile Computing and Communications Review
The political blogosphere and the 2004 U.S. election: divided they blog
Proceedings of the 3rd international workshop on Link discovery
External-memory network analysis algorithms for naturally sparse graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Evaluating Cooperation in Communities with the k-Core Structure
ASONAM '11 Proceedings of the 2011 International Conference on Advances in Social Networks Analysis and Mining
Drawing the AS graph in 2.5 dimensions
GD'04 Proceedings of the 12th international conference on Graph Drawing
Preventing unraveling in social networks: the anchored k-core problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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Degree peeling is used to study complex networks. It corresponds to a decomposition of the graph into vertex groups of increasing minimum degree. However, the peeling value of a vertex is non-local in this context since it relies on the connections the vertex has to groups above it. We explore a different way to decompose a network into edge layers such that the local peeling value of the vertices on each layer does not depend on their non-local connections with the other layers. This corresponds to the decomposition of a graph into subgraphs that are invariant with respect to degree peeling, i.e. they are fixed points. We introduce in this context a method to partition the edges of a graph into fixed points of degree peeling, called the iterative-edge-core decomposition. Information from this decomposition is used to formulate a notion of vertex diversity based on Shannon's entropy. We illustrate the usefulness of this decomposition in social network analysis. Our method can be used for community detection and graph visualization.