Cycle intersection graphs and minimum decycling sets of even graphs

Cary, Michael

doi:10.1142/s1793830920500275

Cited by 2 publications

(2 citation statements)

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“…A unique numeric identifier of this object enables total ordering of cycles. A simple undirected “cycle intersection” graph is created such that each cycle in the original network is represented by a node and each edge connects a pair of cycles that share at least one node [ 50 ] (Fig. 6 a).…”

Section: Methodsmentioning

confidence: 99%

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Nordick

Hong

2021

BMC Bioinformatics

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Background Feedback loops in gene regulatory networks play pivotal roles in governing functional dynamics of cells. Systems approaches demonstrated characteristic dynamical features, including multistability and oscillation, of positive and negative feedback loops. Recent experiments and theories have implicated highly interconnected feedback loops (high-feedback loops) in additional nonintuitive functions, such as controlling cell differentiation rate and multistep cell lineage progression. However, it remains challenging to identify and visualize high-feedback loops in complex gene regulatory networks due to the myriad of ways in which the loops can be combined. Furthermore, it is unclear whether the high-feedback loop structures with these potential functions are widespread in biological systems. Finally, it remains challenging to understand diverse dynamical features, such as high-order multistability and oscillation, generated by individual networks containing high-feedback loops. To address these problems, we developed HiLoop, a toolkit that enables discovery, visualization, and analysis of several types of high-feedback loops in large biological networks. Results HiLoop not only extracts high-feedback structures and visualize them in intuitive ways, but also quantifies the enrichment of overrepresented structures. Through random parameterization of mathematical models derived from target networks, HiLoop presents characteristic features of the underlying systems, including complex multistability and oscillations, in a unifying framework. Using HiLoop, we were able to analyze realistic gene regulatory networks containing dozens to hundreds of genes, and to identify many small high-feedback systems. We found more than a 100 human transcription factors involved in high-feedback loops that were not studied previously. In addition, HiLoop enabled the discovery of an enrichment of high feedback in pathways related to epithelial-mesenchymal transition. Conclusions HiLoop makes the study of complex networks accessible without significant computational demands. It can serve as a hypothesis generator through identification and modeling of high-feedback subnetworks, or as a quantification method for motif enrichment analysis. As an example of discovery, we found that multistep cell lineage progression may be driven by either specific instances of high-feedback loops with sparse appearances, or generally enriched topologies in gene regulatory networks. We expect HiLoop’s usefulness to increase as experimental data of regulatory networks accumulate. Code is freely available for use or extension at https://github.com/BenNordick/HiLoop.

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Section: Methodsmentioning

confidence: 99%

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Nordick

Hong

2021

BMC Bioinformatics

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“…The approach this paper takes is to use cycle decompositions of Eulerian digraphs admitting simple dicycle intersection graphs. Cycle intersection graphs were introduced in [3]. The cycle intersection of an even graph G is a graph CI(G) whose vertex set is the set of cycles in a particular cycle decomposition of G and whose edges represent unique intersections (vertices) of cycles in the cycle decomposition of G. Clearly this concept can be extended to cycle decompositions for Eulerian digraphs.…”

Section: Introductionmentioning

confidence: 99%

Vertices with the second neighborhood property in Eulerian digraphs

Cary¹

2019

Opuscula Math.

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The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple cycle intersection graph have not only adhere to the Second Neighborhood Conjecture, but that local simplicity can, in some cases, also imply the existence of a Seymour vertex in the original digraph.

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Cycle intersection graphs and minimum decycling sets of even graphs

Cited by 2 publications

References 15 publications

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Vertices with the second neighborhood property in Eulerian digraphs

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