Filters








1,187 Hits in 3.9 sec

Dynamics of the threshold model on hypergraphs

Xin-Jian Xu, Shuang He, Li-Jie Zhang
2022 Chaos  
To understand how high-order interactions affect the breakdown of the system, we develop a theoretical framework based on generating function technology to derive the cascade condition and the giant component  ...  In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on hypergraphs.  ...  ACKNOWLEDGMENTS This work was supported by the Natural Science Foundation of China under Grant Nos. 12071281 and 11771277.  ... 
doi:10.1063/5.0075667 pmid:35232049 fatcat:euzg6hdsxvfttchoai6mtydbyi

Hypernetwork Science via High-Order Hypergraph Walks [article]

Sinan G. Aksoy, Cliff Joslyn, Carlos Ortiz Marrero, Brenda Praggastis, Emilie Purvine
2020 arXiv   pre-print
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs.  ...  We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods.  ...  They conduct a rigorous mathematical analysis of the asymptotic s-walk properties of binomial random k-uniform hypergraphs, considering hitting times, the evolution of high-order s-components, and high-order  ... 
arXiv:1906.11295v2 fatcat:qjncpn2oovfqpoaevdl3atxa24

Memetic Multilevel Hypergraph Partitioning [article]

Robin Andre, Sebastian Schlag, Christian Schulz
2018 arXiv   pre-print
Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity.  ...  Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing.  ...  In order to save running time, we choose a subset of 25 hypergraphs shown in Table 2 , k = 32, and ε = 0.03 to evaluate the impact of different algorithmic components of our algorithm (recombine and mutation  ... 
arXiv:1710.01968v2 fatcat:4msekcj2nfa7bgghtqbsr5uxeu

Thresholds for Extreme Orientability [article]

Po-Shen Loh, Rasmus Pagh
2012 arXiv   pre-print
Questions in this area can be phrased in terms of orientations of a graph, or more generally a k-uniform random hypergraph.  ...  for finding an orientation that runs in linear time with high probability, with explicit polynomial bounds on the failure probability.  ...  In the random hypergraph H n,p;k , with probability at least 1 − n −1 , all connected components are of size at most 16k ǫ 2 log n. Proof. Let V be the vertex set of the entire hypergraph.  ... 
arXiv:1202.1111v3 fatcat:tneqnppoerhf5aqv3iae7hc6cu

Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government

Sinan G Aksoy, Aric Hagberg, Cliff A Joslyn, Bill Kay, Emilie Purvine, Stephen J Young
2022 Notices of the American Mathematical Society  
model multi-way relations in hypergraphs, rather than only pairwise interactions in graphs; and (2) challenges posed by modeling networks with extreme sparsity.  ...  The authors are hosting an AMS sponsored Mathematics Research Community (MRC) focusing on two themes that have garnered intense attention in network models of complex relational data: (1) how to faithfully  ...  Indeed, Erd ős and Rényi pointed this out in [ER61] : "The evolution of random graphs may be considered as a (rather simplified) model of the evolution of certain real communication-nets, e.g. the railway  ... 
doi:10.1090/noti2424 fatcat:hnu5w6rojraudjkchhm4k5cdrq

Hypernetwork science via high-order hypergraph walks

Sinan G. Aksoy, Cliff Joslyn, Carlos Ortiz Marrero, Brenda Praggastis, Emilie Purvine
2020 EPJ Data Science  
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs.  ...  We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods.  ...  They conduct a rigorous mathematical analysis of the asymptotic s-walk properties of binomial random k-uniform hypergraphs, considering hitting times, the evolution of high-order s-components, and high-order  ... 
doi:10.1140/epjds/s13688-020-00231-0 fatcat:x7bvvkmbo5gulcoznzjtiialma

Thresholds for Extreme Orientability

Po-Shen Loh, Rasmus Pagh
2013 Algorithmica  
Questions in this area can be phrased in terms of orientations of a graph, or more generally a k-uniform random hypergraph.  ...  -An algorithm for finding an orientation that runs in linear time with high probability, with explicit polynomial bounds on the failure probability.  ...  We also thank the anonymous referees for helpful comments which improved the exposition of this paper.  ... 
doi:10.1007/s00453-013-9749-4 fatcat:al6mxye4c5aqreumn7ekpwez24

Phase transition of random non-uniform hypergraphs

Élie de Panafieu
2015 Journal of Discrete Algorithms  
We analyze their typical structure before, near and after the birth of the "complex" components, that are the connected components with more than one cycle.  ...  Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis.  ...  Finally, we give an intuitive explanation of the birth of the giant component in Section 8 and prove that there is with high probability a component with an unbounded excess in random hypergraphs with  ... 
doi:10.1016/j.jda.2015.01.009 fatcat:xxh3eghn4ratdicbfrwjyedbya

Phase Transition of Random Non-uniform Hypergraphs [chapter]

Élie de Panafieu
2013 Lecture Notes in Computer Science  
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis.  ...  More specifically, we analyze their typical structure before and near the birth of the complex components, that are the connected components with more than one cycle.  ...  As we will see in the proof of Theorem 11, with high probability the kernel of a random hypergraph in the critical window is clean. Lemma 8.  ... 
doi:10.1007/978-3-642-45278-9_12 fatcat:r346m5owafhrtoo45oepwpjo4a

Tensor Entropy for Uniform Hypergraphs [article]

Can Chen, Indika Rajapakse
2020 arXiv   pre-print
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory.  ...  In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data.  ...  Frederick Leve at the Air Force Office of Scientific Research (AFOSR) for support and encouragement.  ... 
arXiv:1912.09624v4 fatcat:d7lyitzgobendimtifh4islyhq

Random Hypergraph Models of Learning and Memory in Biomolecular Networks: Shorter-Term Adaptability vs. Longer-Term Persistency

Byoung-Tak Zhang
2007 2007 IEEE Symposium on Foundations of Computational Intelligence  
performance (learning, adaptability) as opposed to a system consisting of a small number of high-dimensional, fine-tuned, complex components.  ...  We study this issue in a probabilistic hypergraph model called the hypernetworks.  ...  The diversity of the system components can be increased further by incorporating hyperedges of various k's. Figure 7 shows the evolution of the hypergrams in the complete 10-hypernetwork.  ... 
doi:10.1109/foci.2007.371494 dblp:conf/foci/Zhang07 fatcat:yvt2gd3k5zdujcrwrol4rcsxty

Largest components in random hypergraphs [article]

Oliver Cooley, Mihyun Kang, Yury Person
2014 arXiv   pre-print
In this paper we consider j-tuple-connected components in random k-uniform hypergraphs (the j-tuple-connectedness relation can be defined by letting two j-sets be connected if they lie in a common edge  ...  We determine that the existence of a j-tuple-connected component containing Θ (n^j) j-sets in random k-uniform hypergraphs undergoes a phase transition and show that the threshold occurs at edge probability  ...  Vertex-connectivity. First we look at the case of the vertex-connectivity in the random k-uniform hypergraph.  ... 
arXiv:1412.6366v1 fatcat:ck3txfp67vduzmvmch4yzpoasa

Hypergraph Ego-networks and Their Temporal Evolution [article]

Cazamere Comrie, Jon Kleinberg
2021 arXiv   pre-print
The systems these interactions inhabit can be modelled using hypergraphs, a generalization of traditional graphs in which each edge can connect any number of nodes.  ...  In this paper, we propose the study of hypergraph ego-networks, a structure that can be used to model higher-order interactions involving a single node.  ...  BASIC DEFINITIONS Hypergraphs: Hypergraphs are generalizations of traditional pairwise graphs where an edge can connect any number of nodes, whereas an edge in a graph only connect two nodes together  ... 
arXiv:2112.03498v1 fatcat:iuis5atbxbag3kkqxcmp4qkhr4

High-order Phase Transition in Random Hypergrpahs [article]

Linyuan Lu, Xing Peng
2018 arXiv   pre-print
In this paper, we study the high-order phase transition in random r-uniform hypergraphs.  ...  We prove that the sharp threshold of the existence of the s-th-order giant connected components in H^r(n,p) is 1/(r s-1)n r-s. Let c=n r-sp.  ...  Acknowledgment: Authors would like to thank two anonymous referees for their valuable comments which greatly improved the presentation of the paper.  ... 
arXiv:1409.1174v2 fatcat:iqancl3ugbbm5ckppgn7acgpuq

Evolution of Real-world Hypergraphs: Patterns and Models without Oracles [article]

Yunbum Kook, Jihoon Ko, Kijung Shin
2020 arXiv   pre-print
What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?  ...  What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs?  ...  They can represent high-order interactions (i.e., interactions among any number of objects), not just between two as in the graphs.  ... 
arXiv:2008.12729v2 fatcat:m32bkwzucfdppclh4a5sngjrbm
« Previous Showing results 1 — 15 out of 1,187 results