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Table 2 Data sets used in this work

From: Non-backtracking cycles: length spectrum theory and graph mining applications

data set network n k \(\bar {c}\)
Online social (social) Facebook 4k 43.69 0.61
  sdot8 77k 14.13 0.06
  sdot9 82k 14.18 0.06
  Epinions 76k 10.69 0.14
  Twitter 81k 33.02 0.57
  Wiki 7k 28.32 0.14
Coauthorship (CA) AstroPh 19k 21.11 0.63
  CondMat 23k 8.08 0.63
  GrQc 5k 5.53 0.53
  HepPh 12k 19.74 0.61
  HepTh 10k 5.26 0.47
Peer-to-peer file-sharing (P2P) P2P04 11k 7.35 0.01
  P2P05 9k 7.20 0.01
  P2P06 9k 7.23 0.01
  P2P08 6k 6.59 0.01
  P2P09 8k 6.41 0.01
  P2P24 27k 4.93 0.01
  P2P25 23k 4.82 0.01
  P2P30 36k 4.82 0.01
  P2P31 63k 4.73 0.01
Autonomous systems (AS) AS331 11k 4.12 0.30
  AS407 11k 4.10 0.29
  AS414 11k 4.16 0.30
  AS421 11k 4.19 0.30
  AS428 11k 4.13 0.29
  AS505 11k 4.13 0.29
  AS512 11k 4.12 0.29
  AS519 11k 4.11 0.29
  AS526 11k 4.19 0.30
BA-1k   1k 13.90 0.05
CM-1k   1k 10.20 0.17
ER-1k   1k 14.99 0.15
HG-1k   997±2 14.72 0.82
KR-1k   1021±1 14.54 0.03
WS-1k   1k 14.00 0.67
BA-5k   5k 13.98 0.02
CM-5k   5k 11.40 0.13
ER-5k   5k 15.00 0.00
HG-5k   4982±8 14.67 0.82
KR-5k   4089±3 18.27 0.01
WS-5k   5k 14.00 0.67
BA-10k   10k 13.99 0.01
CM-10k   10k 11.97 0.12
ER-10k   10k 14.99 0.00
HG-10k   9958±15 14.96 0.83
KR-10k   8170±11 18.32 0.01
WS-10k   10k 14.00 0.67
  1. n: number of nodes in the largest connected component; 〈k〉: average degree; \(\bar {c}\): average clustering coefficient. Bottom: random graph data sets. We generate 50 graphs of each data set, for a total of 900 random graphs. Top: real networks, grouped in four data sets