Topic
Split graph
About: Split graph is a research topic. Over the lifetime, 3808 publications have been published within this topic receiving 98911 citations.
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TL;DR: This work determines the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population, and shows that the outcome of evolutionary games can depend entirely on the structure of the underlying graph.
Abstract: Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations1,2,3,4. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process3, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks5,6,7. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population7. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.
1,236 citations
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01 Jan 2003TL;DR: As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data, but only very specific graphs such as trees and strings have been considered.
Abstract: As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered.
960 citations
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TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Abstract: A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliques possible in such a graph.
907 citations
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01 Mar 2004
834 citations