The Spectrum of a Random Geometric Graph Is Concentrated
نویسنده
چکیده
Consider n points distributed uniformly in [0, 1]d. Form a graph by connecting two points if their mutual distance is no greater than r(n). This gives a random geometric graph, G(Xn; r(n)), which is connected for appropriate r(n). We show that the spectral measure of the transition matrix of the simple random walk (srw) on G(Xn; r(n)) is concentrated, and in fact converges to that of the graph on the deterministic grid.
منابع مشابه
Generating an Indoor space routing graph using semantic-geometric method
The development of indoor Location-Based Services faces various challenges that one of which is the method of generating indoor routing graph. Due to the weaknesses of purely geometric methods for generating indoor routing graphs, a semantic-geometric method is proposed to cover the existing gaps in combining the semantic and geometric methods in this study. The proposed method uses the CityGML...
متن کاملLaplacian Energy of a Fuzzy Graph
A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...
متن کاملTwo-point concentration in random geometric graphs
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn ∈ R at random (i.i.d. according to some probability distribution ν with a bounded density function) and including an edge between Xi and Xj if ‖Xi−Xj‖ < r where r = r(n) > 0. We prove a conjecture of Penrose ([14]) stating that when r = r(n) is chosen such that nr = o(lnn) then the probability distribution of the cliqu...
متن کاملThe spectrum of the hyper-star graphs and their line graphs
Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...
متن کاملCharacterizations of the simple group $D_{n}(3)$ by prime graph and spectrum
We prove that $D_n(3)$, where $ngeq6$ is even, is uniquely determined by its prime graph. Also, if $G$ is a finite group with the same prime graph as $D_4(3)$, then $Gcong D_4(3), B_3(3), C_3(3)$ or $G/O_2(G)cong {rm Aut}({}^2B_2(8))$.
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 2004