<i>k</i>-Degenerate Graphs

Our goal is to determine the structural differences between different categories of networks and to use these differences to predict the network category. Existing work on this topic has looked at social networks such as Facebook, Twitter, co-author networks etc. We, instead, focus on a novel data set that we have assembled from a variety of sources, including law-enforcement agencies, financial institutions, commercial database providers and other similar organizations. The data set comprises networks of persons of interest with each network belonging to different categories such as suspected terrorists, convicted individuals etc. We demonstrate that such "anti-social" networks are qualitatively different from the usual social networks and that new techniques are required to identify and learn features of such networks for the purposes of prediction and classification.We propose Cliqster, a new generative Bernoulli process-based model for unweighted networks. The generating probabilities are the result of a decomposition which reflects a network's community structure. Using a maximum likelihood solution for the network inference leads to a least-squares problem. By solving this problem, we are able to present an efficient algorithm for transforming the network to a new space which is both concise and discriminative. This new space preserves the identity of the network as much as possible. Our algorithm is interpretable and intuitive. Finally, by comparing our research against the baseline method (SVD) and against a state-of-the-art Graphlet algorithm, we show the strength of our algorithm in discriminating between different categories of networks.

show abstract

“…The 41]. In [40] they proposed a variation of the Bron-Kerbosch algorithm, which runs in O(f n3 f /3 ) where f is a network's degeneracy number.…”

Section: Complexitymentioning

confidence: 99%

The network you keep: Analyzing persons of interest using cliqster

Fadaee

Farajtabar

Sundaram

et al. 2014

2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2014)

View full text Add to dashboard Cite

show abstract

“…The peeling value of G is also called the degeneracy of G [14]. For a graph of peeling value k, its vertices can be ordered in a sequence (v 1 , .…”

Section: Peeling Values and Fixed Pointsmentioning

confidence: 99%

Fixed points of graph peeling

Abello

Queyroi

2013

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining

View full text Add to dashboard Cite

Abstract-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 iterativeedge-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.

show abstract

“…A graph G for which col(G) ≤ k + 1 has also been called k-degenerate by Lick and White [88]. (A graph is k-degenerate if every induced subgraph has minimum degree at most k.) A related concept has been studied in the social and biological network literature as the k-core of a graph [21,105].…”

Section: The Coloringmentioning

confidence: 99%

What Color Is Your Jacobian? Graph Coloring for Computing Derivatives

Gebremedhin¹,

Manne²,

Pothen³

2005

SIAM Rev.

232

174

View full text Add to dashboard Cite

Abstract. Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specifics of the computational techniques employed. We consider eight variant vertex coloring problems here. This article begins with a gentle introduction to the problem of computing a sparse Jacobian, followed by an overview of the historical development of the research area. Then we present a unifying framework for the graph models of the variant matrix estimation problems. The framework is based upon the viewpoint that a partition of a matrix into structurally orthogonal groups of columns corresponds to distance-2 coloring an appropriate graph representation. The unified framework helps integrate earlier work and leads to fresh insights; enables the design of more efficient algorithms for many problems; leads to new algorithms for others; and eases the task of building graph models for new problems. We report computational results on two of the coloring problems to support our claims. Most of the methods for these problems treat a column or a row of a matrix as an atomic entity, and partition the columns or rows (or both). A brief review of methods that do not fit these criteria is provided. We also discuss results in discrete mathematics and theoretical computer science that intersect with the topics considered here.

show abstract

k-Degenerate Graphs

Cited by 231 publications

References 7 publications

The network you keep: Analyzing persons of interest using cliqster

The network you keep: Analyzing persons of interest using cliqster

Fixed points of graph peeling

What Color Is Your Jacobian? Graph Coloring for Computing Derivatives

Contact Info

Product

Resources

About