Core (graph theory)

About: Core (graph theory) is a research topic. Over the lifetime, 853 publications have been published within this topic receiving 8645 citations. The topic is also known as: core of a graph.

Coverings of Bipartite Graphs

Abstract: For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core. It is also possible to decompose the core into irreducible parts and thus obtain a canonical reduction of the graph. The concept of irreducibility is very easily and naturally expressed in terms of exterior coverings. The role of the inadmissible edges of a graph is to obstruct certain natural coverings of the graph.

Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects.

Abstract: Exponential-family random graph models (ERGMs) represent the processes that govern the formation of links in networks through the terms selected by the user. The terms specify network statistics that are sufficient to represent the probability distribution over the space of networks of that size. Many classes of statistics can be used. In this article we describe the classes of statistics that are currently available in the ergm package. We also describe means for controlling the Markov chain Monte Carlo (MCMC) algorithm that the package uses for estimation. These controls affect either the proposal distribution on the sample space used by the underlying Metropolis-Hastings algorithm or the constraints on the sample space itself. Finally, we describe various other arguments to core functions of the ergm package.

Analysis of a greedy active learning strategy

Abstract: We abstract out the core search problem of active learning schemes, to better understand the extent to which adaptive labeling can improve sample complexity. We give various upper and lower bounds on the number of labels which need to be queried, and we prove that a popular greedy active learning rule is approximately as good as any other strategy for minimizing this number of labels.

A practical framework for the abstract interpretation of logic programs

Abstract: There are numerous papers concerned with the compile-time derivation of certain run-time properties of logic programs, e.g. mode inferencing, type checking, type synthesis, and properties relevant for and -parallel execution. Most approaches have little in common, they are developed in an ad hoc way, and their correctness is not always obvious. We develop a general framework which is suited to develop complex applications and to prove their correctness. All states which are possible at run time can be represented by an infinite set of proof trees ( and trees, SLD derivations). The core idea of our approach is to represent this infinite set of and trees by a finite abstract and-or graph. We present a generic abstract interpretation procedure for the construction of such an abstract and-or graph and formulate conditions which allow us to construct a correct one in finite time.

Core-periphery organization of complex networks.

Abstract: Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. Among other things we conclude that geographically embedded transportation networks have a strong core-periphery structure. We proceed to study radial statistics of the core, i.e., properties of the neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n neighborhoods at a certain distance from the core suggesting an effective radius for nontrivial network processes.