Characterization of L-norm Statistic for Anomaly Detection in Erdős Rényi Graphs
نویسندگان
چکیده
We devise statistical tests to detect the presence of an embedded ErdősRényi (ER) subgraph inside a random graph, which is also an ER graph. We make use of properties of the asymptotic distribution of eigenvectors of random graphs to detect the subgraph. This problem is related to the planted clique problem that is of considerable interest.
منابع مشابه
Characterization of L1-norm statistic for anomaly detection in Erdős Rényi graphs
We describe a test statistic based on the Lnorm of the eigenvectors of a modularity matrix to detect the presence of an embedded Erdős Rényi (ER) subgraph inside a larger ER random graph. An embedded subgraph may model a hidden community in a large network such as a social network or a computer network. We make use of the properties of the asymptotic distribution of eigenvectors of random graph...
متن کاملLifshits Tails for Spectra of Erdős-rényi Random Graphs by Oleksiy Khorunzhiy
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
متن کاملLifshits Tails for Spectra of Erdős-rényi Random Graphs
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
متن کاملLifshitz Tails for Spectra of Erdős–rényi Random Graphs
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshitz-tail behavior at the lower spectra...
متن کاملMajority-vote on directed Erdős–Rényi random graphs
Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter qc, as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016