Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

被引:1
作者
Garrod, Matthew [1 ]
Jones, Nick S. [1 ]
机构
[1] Imperial Coll, Dept Math, London SW7 2AZ, England
基金
英国工程与自然科学研究理事会;
关键词
SYNCHRONIZATION; CONSENSUS;
D O I
10.1103/PhysRevE.98.052316
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
A random geometric graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the distributional properties of the algebraic connectivity which is informative of diffusion and synchronization time scales in graphs. We use numerical simulations to provide a characterization of the algebraic connectivity distribution for RGG ensembles. We find that the algebraic connectivity can show fluctuations relative to its mean on the order of 30%, even for relatively large RGG ensembles (N = 10(5)). We explore the factors driving these fluctuations for RGG ensembles with different choices of dimensionality, boundary conditions, and node distributions. Within a given ensemble, the algebraic connectivity can covary with the minimum degree and can also be affected by the presence of density inhomogeneities in the nodal distribution. We also derive a closed-form expression for the expected algebraic connectivity for RGGs with periodic boundary conditions for general dimension.
引用
收藏
页数:11
相关论文
共 51 条
  • [1] Weighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix
    Alonso, L.
    Mendez-Bermudez, J. A.
    Gonzalez-Melendrez, A.
    Moreno, Yamir
    [J]. JOURNAL OF COMPLEX NETWORKS, 2018, 6 (05) : 753 - 766
  • [2] [Anonymous], 14 INT PROB WORKSH
  • [3] [Anonymous], 2016, PROC IEEE GLOBAL COM
  • [4] Network synchronization: Spectral versus statistical properties
    Atay, Fatihcan M.
    Biyikoglu, Tuerker
    Jost, Juergen
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2006, 224 (1-2) : 35 - 41
  • [5] Badiu MA, 2018, IEEE INT SYMP INFO, P2137, DOI 10.1109/ISIT.2018.8437912
  • [6] Barbarossa S, 2007, INT CONF ACOUST SPEE, P841
  • [7] Spatially embedded random networks
    Barnett, L.
    Di Paolo, E.
    Bullock, S.
    [J]. PHYSICAL REVIEW E, 2007, 76 (05)
  • [8] Spatial networks
    Barthelemy, Marc
    [J]. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2011, 499 (1-3): : 1 - 101
  • [9] Dimensionality of Social Networks Using Motifs and Eigenvalues
    Bonato, Anthony
    Gleich, David F.
    Kim, Myunghwan
    Mitsche, Dieter
    Pralat, Pawel
    Tian, Yanhua
    Young, Stephen J.
    [J]. PLOS ONE, 2014, 9 (09):
  • [10] Eigenvalues of Euclidean Random Matrices
    Bordenave, Charles
    [J]. RANDOM STRUCTURES & ALGORITHMS, 2008, 33 (04) : 515 - 532