Caenorhabditis elegans (neural)
This is a weighted directed network representing the neural network of
Caenorhabditis elegans. The original network had directed edges
allowing multiple parallel edges with integer weights. In this version, the
network is undirected, allows no multiple edges, and the given edge weights are
the sum of the original edge weights. As described in the original publication
by J. G. White and colleagues, the data was assembled by hand and may contain a
small number of errors. To cite: "We are reasonably confident that the
structure that we present is substantially correct and gives a reasonable
picture of the organization of the nervous system in a typical C.
elegans hermaphrodite."
Metadata
Statistics
Size  n =  297

Volume  m =  4,296

Loop count  l =  0

Wedge count  s =  53,804

Claw count  z =  7,341,160

Cross count  x =  307,724,064

Triangle count  t =  3,241

Square count  q =  44,636

4Tour count  T_{4} =  576,600

Maximum degree  d_{max} =  268

Maximum outdegree  d^{+}_{max} =  134

Maximum indegree  d^{−}_{max} =  134

Average degree  d =  28.929 3

Fill  p =  0.048 867 0

Size of LCC  N =  297

Size of LSCC  N_{s} =  297

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

Diameter  δ =  5

50Percentile effective diameter  δ_{0.5} =  1.929 02

90Percentile effective diameter  δ_{0.9} =  2.891 73

Median distance  δ_{M} =  2

Mean distance  δ_{m} =  2.469 83

Gini coefficient  G =  0.385 480

Balanced inequality ratio  P =  0.362 430

Outdegree balanced inequality ratio  P_{+} =  0.362 430

Indegree balanced inequality ratio  P_{−} =  0.362 430

Relative edge distribution entropy  H_{er} =  0.950 953

Power law exponent  γ =  1.421 43

Tail power law exponent  γ_{t} =  3.341 00

Tail power law exponent with p  γ_{3} =  3.341 00

pvalue  p =  0.658 000

Outdegree tail power law exponent with p  γ_{3,o} =  3.341 00

Outdegree pvalue  p_{o} =  0.661 000

Indegree tail power law exponent with p  γ_{3,i} =  3.341 00

Indegree pvalue  p_{i} =  0.649 000

Degree assortativity  ρ =  −0.163 199

Degree assortativity pvalue  p_{ρ} =  4.990 05 × 10^{−27}

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

Clustering coefficient  c =  0.180 711

Directed clustering coefficient  c^{±} =  0.180 711

Spectral norm  α =  412.892

Operator 2norm  ν =  206.446

Cyclic eigenvalue  π =  206.446

Algebraic connectivity  a =  1.883 17

Spectral separation  λ_{1}[A] / λ_{2}[A] =  1.234 66

Reciprocity  y =  1.000 00

Nonbipartivity  b_{A} =  0.473 226

Normalized nonbipartivity  b_{N} =  0.451 282

Algebraic nonbipartivity  χ =  0.843 939

Spectral bipartite frustration  b_{K} =  0.014 586 2

Controllability  C =  15

Relative controllability  C_{r} =  0.050 505 1

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 ]

[2]

Duncan J. Watts and Steven H. Strogatz.
Collective dynamics of `smallworld' networks.
Nature, 393(1):440–442, 1998.

[3]

John G. White, E. Southgate, J. N. Thomson, and S. Brenner.
The structure of the nervous system of the nematode Caenorhabditis
elegans.
Phil. Trans. R. Soc. Lond, 314:1–340, 1986.
