Great Lakes
This is the directed road network from the 9th DIMACS Implementation Challenge,
for the area "Great Lakes".
Metadata
Statistics
Size  n =  2,758,119

Volume  m =  6,794,808

Loop count  l =  0

Wedge count  s =  6,157,714

Claw count  z =  44,551,232

Cross count  x =  42,027,094

Triangle count  t =  47,051

Square count  q =  224,038

4Tour count  T_{4} =  33,217,968

Maximum degree  d_{max} =  16

Maximum outdegree  d^{+}_{max} =  8

Maximum indegree  d^{−}_{max} =  8

Average degree  d =  4.927 13

Fill  p =  8.932 05 × 10^{−7}

Size of LCC  N =  2,758,119

Size of LSCC  N_{s} =  2,758,119

Relative size of LSCC  N^{r}_{s} =  1.000 00

Diameter  δ =  4,127

50Percentile effective diameter  δ_{0.5} =  1,104.33

90Percentile effective diameter  δ_{0.9} =  2,377.70

Median distance  δ_{M} =  1,105

Mean distance  δ_{m} =  1,239.73

Gini coefficient  G =  0.205 838

Balanced inequality ratio  P =  0.423 419

Outdegree balanced inequality ratio  P_{+} =  0.423 419

Indegree balanced inequality ratio  P_{−} =  0.423 419

Relative edge distribution entropy  H_{er} =  0.994 915

Power law exponent  γ =  2.225 85

Tail power law exponent  γ_{t} =  6.141 00

Tail power law exponent with p  γ_{3} =  6.141 00

pvalue  p =  0.000 00

Outdegree tail power law exponent with p  γ_{3,o} =  6.141 00

Outdegree pvalue  p_{o} =  0.000 00

Indegree tail power law exponent with p  γ_{3,i} =  6.141 00

Indegree pvalue  p_{i} =  0.000 00

Degree assortativity  ρ =  +0.096 074 9

Degree assortativity pvalue  p_{ρ} =  0.000 00

In/outdegree correlation  ρ^{±} =  +1.000 00

Clustering coefficient  c =  0.022 923 0

Directed clustering coefficient  c^{±} =  0.022 923 0

Spectral norm  α =  9.039 66

Operator 2norm  ν =  4.519 83

Cyclic eigenvalue  π =  4.519 83

Algebraic connectivity  a =  1.167 59 × 10^{−7}

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.054 40

Reciprocity  y =  1.000 00

Nonbipartivity  b_{A} =  0.126 633

Normalized nonbipartivity  b_{N} =  7.028 07 × 10^{−5}

Algebraic nonbipartivity  χ =  0.000 141 024

Spectral bipartite frustration  b_{K} =  1.431 10 × 10^{−5}

Controllability  C =  272,331

Relative controllability  C_{r} =  0.098 737 9

Plots
Matrix decompositions plots
Downloads
References
[1]

Jérôme Kunegis.
KONECT – The Koblenz Network Collection.
In Proc. Int. Conf. on World Wide Web Companion, pages
1343–1350, 2013.
[ http ]
