The size of the largest strongly connected component of a random digraph with a given degree sequence

被引：52
|
作者：
Cooper, C [1 ]
Frieze, A
机构：
[1] Univ London Goldsmiths Coll, Dept Math & Comp Sci, London SW14 6NW, England
[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
来源：
COMBINATORICS PROBABILITY & COMPUTING | 2004年 / 13卷 / 03期
关键词：
D O I：
10.1017/S096354830400611X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We give results on the strong connectivity for spaces of sparse random digraphs specified by degree sequence. A full characterization is provided, in probability, of the fan-in and fan-out of all vertices including the number of vertices with small (o(n)) and large (cn) fan-in or fan-out. We also give the size of the giant strongly connected component, if any, and the structure of the bow-tie digraph induced by the vertices with large fan-in or fan-out. Our results follow a direct analogy of the extinction probabilities of classical branching processes.
引用
收藏
页码：319 / 337
页数：19
相关论文
共 48 条
  • [1] Largest component of subcritical random graphs with given degree sequence*
    Coulson, Matthew
    Perarnau, Guillem
    ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28 : 1 - 28
  • [2] The size of the giant component of a random graph with a given degree sequence
    Molloy, M
    Reed, B
    COMBINATORICS PROBABILITY & COMPUTING, 1998, 7 (03): : 295 - 305
  • [3] ON THE LARGEST COMPONENT OF THE CRITICAL RANDOM DIGRAPH
    Coulson, M.
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2019, 88 (03): : 567 - 572
  • [4] THE COMPONENT SIZES OF A CRITICAL RANDOM GRAPH WITH GIVEN DEGREE SEQUENCE
    Joseph, Adrien
    ANNALS OF APPLIED PROBABILITY, 2014, 24 (06): : 2560 - 2594
  • [5] BIRTH OF A STRONGLY CONNECTED GIANT IN AN INHOMOGENEOUS RANDOM DIGRAPH
    Bloznelis, Mindaugas
    Goetze, Friedrich
    Jaworski, Jerzy
    JOURNAL OF APPLIED PROBABILITY, 2012, 49 (03) : 601 - 611
  • [6] THE LARGEST CONNECTED COMPONENT IN A RANDOM MAPPING
    JAWORSKI, J
    MUTAFCHIEV, L
    RANDOM STRUCTURES & ALGORITHMS, 1994, 5 (01) : 73 - 94
  • [7] Generating random networks that consist of a single connected component with a given degree distribution
    Tishby, Ido
    Biham, Ofer
    Katzav, Eytan
    Kuehn, Reimer
    PHYSICAL REVIEW E, 2019, 99 (04)
  • [8] ON THE LARGEST TREE OF GIVEN MAXIMUM DEGREE IN A CONNECTED GRAPH
    CARO, Y
    KRASIKOV, I
    RODITTY, Y
    JOURNAL OF GRAPH THEORY, 1991, 15 (01) : 7 - 13
  • [9] RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE
    Chatterjee, Sourav
    Diaconis, Persi
    Sly, Allan
    ANNALS OF APPLIED PROBABILITY, 2011, 21 (04): : 1400 - 1435
  • [10] Emergence and Size of the Giant Component in Clustered Random Graphs with a Given Degree Distribution
    Berchenko, Yakir
    Artzy-Randrup, Yael
    Teicher, Mina
    Stone, Lewi
    PHYSICAL REVIEW LETTERS, 2009, 102 (13)
12345