Algebraic non-bipartivity

These are the values of the algebraic non-bipartivity (χ) for all networks to which the statistic applies and for which it was computed. In total, it has been computed for 137 networks.

The algebraic non-bipartivity (χ) is the smallest eigenvalue of the signless Laplacian matrix K = D + A. It is zero if and only if at least one connected component of the graph is bipartite. It serves as the basis for the spectral bipartite frustration, a measure of the bipartivity of a graph.

The full definition of the algebraic non-bipartivity as well as its properties and relationships to other graph statistics can be found in the KONECT handbook.

References for this statistic:

[1] Jérôme Kunegis. Exploiting the structure of bipartite graphs for algebraic and spectral graph theory applications. Internet Math., 11(3):201–321, 2015. [ http ]

NameAttributesχ
HIV
0.008 041 22
Zachary karate club
0.878 988
Highland tribes
2.375 14
Taro exchange
1.051 84
Zebra
1.527 21
Kangaroos
0.904 799
Iceland
0.081 474 0
Contiguous USA
0.483 588
Rhesus macaques
2.647 03
Dolphins
0.528 476
Chesapeake Bay
1.747 51
Crisis in a Cloister
6.265 51
Cattle
0.941 479
PDZBase
0.006 661 35
Pro League (2016/2017)
11.269 5
Train bombing
0.831 432
Sheep
3.653 32
Gene fusion
0.013 441 4
Les Misérables
0.240 638
Bundesliga (2016/2017)
12.256 3
Bison
5.508 78
David Copperfield
0.675 374
Windsurfers
5.586 32
Political books
1.276 20
Seventh graders
6.271 56
Ligue 1 (2016/2017)
14.544 9
Premier League (2013/2014)
13.167 0
Highschool
1.466 37
Hens
30.000 0
American football
5.077 40
Similarities (DBpedia)
0.130 995
Congress votes
0.358 762
Physicians
1.505 05
Japanese macaques
16.311 6
Euroroads
0.008 094 25
FilmTrust trust
0.059 906 8
Caenorhabditis elegans (metabolic)
0.293 557
Jazz musicians
0.692 773
Yeast
0.028 868 1
Little Rock Lake
0.974 193
LiquidFeedback (units)
0.012 882 5
Network science
0.462 123
Air traffic control
0.025 807 5
Residence hall
1.783 97
Facebook (NIPS)
0.003 114 08
A Song of Ice and Fire
0.203 828
LiquidFeedback (global)
0.007 000 89
Wikipedia talk (ht)
0.194 136
Caenorhabditis elegans
0.293 559
Hamsterster households
0.212 564
Caenorhabditis elegans (neural)
0.843 939
U. Rovira i Virgili
0.334 159
Florida ecosystem wet
1.907 39
Florida ecosystem dry
1.906 87
Dutch college
5.864 12
Human proteins (Stelzl)
0.025 524 6
Human proteins (Vidal)
0.107 163
Human proteins (Figeys)
0.104 135
US power grid
0.016 118 7
Bible
0.983 261
Hamsterster friendships
0.032 135 6
Erdős
0.024 521 8
Hamsterster friends
0.032 135 6
Route views
0.089 770 8
DNC co-recipients
0.368 608
Hamsterster full
0.193 235
Adolescent health
0.319 993
Blogs
0.375 440
LiquidFeedback (issues)
0.111 149
LiquidFeedback (areas)
0.097 111 8
Gnutella (08)
0.073 763 8
Sister cities
0.012 754 3
Wikipedia talk (cy)
0.068 781 7
Wikipedia talk (oc)
0.125 065
Pretty Good Privacy
0.018 345 5
Gnutella (09)
0.068 085 9
Political blogs
0.299 050
Wikipedia talk (br)
0.196 562
OpenFlights (Opsahl)
0.052 326 2
Gnutella (06)
0.183 577
Gnutella (05)
0.199 937
US airports
0.246 652
Twitter lists
0.005 056 39
CiaoDVD trust
0.107 350
Infectious
0.645 453
Gnutella (04)
0.040 791 0
Hypertext 2009
0.989 464
Haggle
0.827 831
Chicago
0.051 149 7
LiquidFeedback (all)
0.135 392
Google+ (NIPS)
0.011 413 1
LiquidFeedback (temporal)
0.135 392
Autonomous systems (DIMACS10)
0.071 860 9
CAIDA
0.020 451 8
Wikipedia talk (nds)
0.017 531 0
Wikipedia talk (eo)
0.100 022
Wikipedia links (gag)
0.266 318
Wikipedia links (am)
0.061 934 2
Wikipedia links (mi)
0.218 368
Wikipedia talk (eu)
0.007 430 54
Wikipedia talk (gl)
0.297 571
Wikipedia talk (lv)
0.026 898 5
Wikipedia links (gan)
0.045 368 0
Wikipedia links (nah)
0.084 319 2
Wikipedia links (rue)
0.154 463
Wikipedia links (lez)
0.151 220
Condensed matter (2005)
0.088 251 8
Wikipedia links (as)
0.013 493 7
Wikipedia links (si)
0.010 756 7
Wikipedia links (xal)
0.019 913 2
Wikipedia links (se)
0.077 046 5
Wikipedia talk (bn)
0.024 876 4
Wikipedia links (hsb)
0.076 119 2
Wikipedia links (os)
0.196 428
Wikipedia talk (sk)
0.059 074 1
Wikipedia links (hif)
0.136 427
Wikipedia links (diq)
0.065 837 5
Wikipedia links (cdo)
0.000 245 456
Wikipedia links (kn)
0.059 593 7
Wikipedia links (map-bms)
0.076 848 3
Wikipedia links (bcl)
0.097 819 1
Wikipedia links (gd)
0.108 045
Wikipedia links (bh)
0.056 609 5
Wikipedia links (li)
0.006 660 56
Wikipedia talk (el)
0.049 156 6
Wikipedia talk (sr)
0.024 720 5
Wikipedia talk (ca)
0.145 677
Wikipedia talk (sv)
0.166 034
Wikipedia talk (vi)
0.014 534 6
Wikipedia talk (ja)
0.053 922 5
Wikipedia talk (pl)
0.106 509
Wikipedia talk (nl)
0.043 211 4
Wikipedia talk (ru)
0.087 219 0
Wikipedia talk (pt)
0.031 297 6
Wikipedia talk (zh)
0.029 891 8
Wikipedia talk (es)
0.043 537 3
Wikipedia talk (de)
0.033 969 5