Filtering Statistics on Networks
Abstract
:1. Introduction
2. Filtering Statistics on a Ring
2.1. Degeneracy Distribution
2.2. Effect of Filter Length
3. Filtering on Graphs
3.1. Degeneracy Distributions
3.2. Behaviour of Important Quantities
4. Discussion
5. Materials and Methods
5.1. Calculation of Degeneracy Distributions
5.2. Asymptotics of the Degeneracy Distribution on Rings
Author Contributions
Funding
Conflicts of Interest
Appendix A. Further Results for the Weak Rule Filter
Graph | n | |||||
---|---|---|---|---|---|---|
Apollonian 2 | 7 | 1.95461 | 1.21901 | 1.91660 | 0.11519 | 0.66045 |
Apollonian 3 | 16 | 1.94788 | 1.43435 | 1.91189 | 0.09594 | 0.64711 |
(3,5)-cage | 10 | 1.91202 | 1.21481 | 1.84295 | 0.13705 | 0.62974 |
(3,6)-cage | 14 | 1.91394 | 1.34590 | 1.83757 | 0.12271 | 0.63149 |
(3,7)-cage | 24 | 1.91348 | 1.25055 | 1.83511 | 0.11462 | 0.63259 |
(3,8)-cage | 30 | 1.91330 | 1.34897 | 1.83337 | 0.10559 | 0.63275 |
(4,5)-cage | 19 | 1.95248 | 1.21101 | 1.91027 | 0.08217 | 0.65878 |
(4,6)-cage | 26 | 1.95322 | 1.37995 | 1.91085 | 0.07188 | 0.65902 |
(5,5)-cage 1 | 30 | 1.97461 | 1.16392 | 1.95220 | 0.04494 | 0.67453 |
(5,5)-cage 2 | 30 | 1.97461 | 1.18854 | 1.95219 | 0.04495 | 0.67453 |
(5,5)-cage 3 | 30 | 1.97461 | 1.21540 | 1.95220 | 0.04496 | 0.67453 |
(5,5)-cage 4 | 30 | 1.97461 | 1.17585 | 1.95220 | 0.04495 | 0.67453 |
torus | 9 | 1.95698 | 1.16653 | 1.92324 | 0.10088 | 0.66192 |
torus | 16 | 1.95546 | 1.38485 | 1.92191 | 0.09024 | 0.65777 |
torus | 25 | 1.95475 | 1.21993 | 1.91904 | 0.08076 | 0.65828 |
torus | 30 | 1.95475 | 1.28517 | 1.91898 | 0.07568 | 0.65831 |
torus | 30 | 1.95626 | 1.22522 | 1.91924 | 0.07072 | 0.66127 |
torus | 32 | 1.95510 | 1.38392 | 1.91932 | 0.07475 | 0.65813 |
torus | 36 | 1.95475 | 1.38400 | 1.91883 | 0.07034 | 0.65833 |
SWB(3) | 10 | 1.91492 | 1.35588 | 1.85212 | 0.14568 | 0.62873 |
SWB(3) | 20 | 1.91523 | 1.30100 | 1.84849 | 0.12731 | 0.62956 |
SWB(3) | 30 | 1.91523 | 1.35620 | 1.84851 | 0.11281 | 0.62956 |
SWB(4) | 12 | 1.95603 | 1.17605 | 1.91983 | 0.09152 | 0.66087 |
SWB(4) | 21 | 1.95626 | 1.21231 | 1.91923 | 0.08079 | 0.66127 |
SWB(4) | 30 | 1.95626 | 1.20790 | 1.91924 | 0.07071 | 0.66127 |
SWB(5) | 12 | 1.97929 | 1.17605 | 1.96131 | 0.05848 | 0.67803 |
SWB(5) | 20 | 1.97927 | 1.16442 | 1.96025 | 0.04881 | 0.67840 |
SWB(5) | 32 | 1.97927 | 1.14893 | 1.96021 | 0.04144 | 0.67842 |
RRG(2) | 10 | 1.76075 | 1.33214 | 1.62827 | 0.16029 | 0.53010 |
RRG(2) | 20 | 1.81141 | 1.29593 | 1.65746 | 0.14345 | 0.56553 |
RRG(2) | 30 | 1.83115 | 1.27447 | 1.67090 | 0.11728 | 0.58305 |
RRG(3) | 10 | 1.86350 | 1.31014 | 1.73760 | 0.18497 | 0.59914 |
RRG(3) | 20 | 1.88987 | 1.28690 | 1.78608 | 0.13766 | 0.61721 |
RRG(3) | 30 | 1.89895 | 1.27941 | 1.80483 | 0.11537 | 0.62310 |
RRG(4) | 10 | 1.92754 | 1.24293 | 1.86647 | 0.13602 | 0.64106 |
RRG(4) | 20 | 1.93917 | 1.25076 | 1.88272 | 0.09610 | 0.65019 |
RRG(4) | 30 | 1.94507 | 1.25247 | 1.89654 | 0.07819 | 0.65347 |
RRG(5) | 10 | 1.93764 | 1.26982 | 1.88340 | 0.12318 | 0.64808 |
RRG(5) | 20 | 1.95952 | 1.23790 | 1.92369 | 0.07520 | 0.66371 |
RRG(5) | 30 | 1.96616 | 1.22872 | 1.93641 | 0.05720 | 0.66839 |
SW(3) | 10 | 1.90692 | 1.25638 | 1.82855 | 0.15381 | 0.62737 |
SW(3) | 20 | 1.90025 | 1.27244 | 1.80865 | 0.13264 | 0.62404 |
SW(3) | 30 | 1.91093 | 1.27260 | 1.82941 | 0.10905 | 0.63105 |
SW(4) | 10 | 1.91972 | 1.26865 | 1.85154 | 0.14500 | 0.63556 |
SW(4) | 20 | 1.93992 | 1.25544 | 1.88853 | 0.09904 | 0.64926 |
SW(4) | 30 | 1.94584 | 1.26608 | 1.89776 | 0.07874 | 0.65403 |
SW(5) | 10 | 1.94942 | 1.23419 | 1.90650 | 0.11008 | 0.65650 |
SW(5) | 20 | 1.96150 | 1.23542 | 1.92709 | 0.07365 | 0.66525 |
SW(5) | 30 | 1.96889 | 1.23140 | 1.94184 | 0.05471 | 0.67024 |
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Pattern | D | ||||||
---|---|---|---|---|---|---|---|
0 (or 1) | 2 | 1 | 2 | 0 | 0.69315 | 1 | |
00 | 1.75488 | 1.61803 | 1.61803 | 0.18261 | 0.48468 | 924(1) | |
10 | 1.61803 | 1.31951 | 1 | 0.13954 | 0.46986 | 513(1) | |
010 | 1.61803 | 1.75488 | 1.46557 | 0.17248 | 0.35187 | 777 | |
000 | 1.61803 | 1.83929 | 1.49710 | 0.1453(1) | 0.30105 | 554(2) | |
0110 | 1.46557 | 1.86676 | 1.22074 | 0.11881 | 0.22387 | 698 | |
0100 | |||||||
0000 | 1.52895 | 1.92756 | 1.41963(2) | 0.08856 | 0.17673 | 311 | |
00100 | 1.46557 | 1.9417 | 1.38028 | 0.06434 | 0.13371 | 291 | |
01110 | 1.38028 | 1.93318 | 1.16730 | 0.06312 | 0.13562 | 255 | |
01100 | |||||||
01000 | |||||||
01010 | 1.44327 | 1.94789 | 1.32472 | 0.06117 | 0.12584 | 301 | |
00000 | 1.46557(2) | 1.96595 | 1.3652(2) | 0.05108 | 0.10052 | 190 | |
001100 | 1.38028 | 1.96931 | 1.2499(2) | 0.03606 | 0.07899 | 197 | |
001000 | |||||||
010010 | 1.37108(1) | 1.97113 | 1.1938(5) | 0.03586 | 0.07692 | 218 | |
011110 | 1.32472 | 1.96717 | 1.13472 | 0.03448 | 0.07939 | 123 | |
011100 | |||||||
011010 | |||||||
011000 | |||||||
010100 | |||||||
010000 | |||||||
000000 | 1.4176(2) | 1.98358 | 1.32486 | 0.02968 | 0.05606 | 123 | |
0110110 | 1.32472 | 1.98574 | 1.158(2) | 0.02084 | 0.04353 | 129 | |
0111110 | 1.28520 | 1.98386 | 1.11278 | 0.02016 | 0.04535 | 64 | |
0111010 | |||||||
01111110 | 1.25542 | 1.99203 | 1.09698 | 0.01213 | 0.02546 | 36 | |
011111110 | 1.23205 | 1.99605 | 1.08507 | 0.00727 | 0.01411 | 25 | |
0111111110 | 1.21315 | 1.99803 | 1.07577 | 0.00427 | 0.00774 | 16 |
Graph | n | |||||
---|---|---|---|---|---|---|
Apollonian 2 | 7 | 1.47236 | 1.94420 | 1.40854 | 0.08504 | 0.12919 |
Apollonian 3 | 16 | 1.52380 | 1.94596 | 1.49013 | 0.08148 | 0.13005 |
(3,5)-cage | 10 | 1.54199 | 1.88916 | 1.42694 | 0.10463 | 0.22185 |
(3,6)-cage | 14 | 1.54904 | 1.88549 | 1.46952 | 0.09741 | 0.22302 |
(3,7)-cage | 24 | 1.54516 | 1.88688 | 1.42191 | 0.12412 | 0.22268 |
(3,8)-cage | 30 | 1.54618 | 1.88722 | 1.44630 | 0.08763 | 0.22254 |
(4,5)-cage | 19 | 1.48991 | 1.94458 | 1.37494 | 0.08094 | 0.13458 |
(4,6)-cage | 26 | 1.50129 | 1.94386 | 1.44997 | 0.05243 | 0.13497 |
(5,5)-cage 1 | 30 | 1.44928 | 1.97192 | 1.34932 | 0.04164 | 0.07890 |
(5,5)-cage 2 | 30 | 1.44984 | 1.97191 | 1.35558 | 0.04602 | 0.07891 |
(5,5)-cage 3 | 30 | 1.44954 | 1.97192 | 1.35543 | 0.04201 | 0.07890 |
(5,5)-cage 4 | 30 | 1.44964 | 1.97191 | 1.35280 | 0.05264 | 0.07891 |
torus | 9 | 1.47967 | 1.94480 | 1.42350 | 0.07165 | 0.13112 |
torus | 16 | 1.51160 | 1.94843 | 1.46895 | 0.06205 | 0.13043 |
torus | 25 | 1.50066 | 1.94752 | 1.41779 | 0.05857 | 0.13132 |
torus | 30 | 1.50206 | 1.94754 | 1.42286 | 0.06159 | 0.13131 |
torus | 30 | 1.48922 | 1.94678 | 1.39796 | 0.05933 | 0.13100 |
torus | 32 | 1.50701 | 1.94785 | 1.44980 | 0.06251 | 0.13096 |
torus | 36 | 1.50405 | 1.94756 | 1.44490 | 0.05890 | 0.13130 |
SWB(3) | 10 | 1.55564 | 1.89336 | 1.48457 | 0.10987 | 0.21539 |
SWB(3) | 20 | 1.55376 | 1.89450 | 1.46394 | 0.09850 | 0.21540 |
SWB(3) | 30 | 1.55377 | 1.89450 | 1.46573 | 0.10256 | 0.21541 |
SWB(4) | 12 | 1.48818 | 1.94653 | 1.40063 | 0.07107 | 0.13103 |
SWB(4) | 21 | 1.48924 | 1.94678 | 1.39802 | 0.06401 | 0.13100 |
SWB(4) | 30 | 1.48922 | 1.94678 | 1.39797 | 0.06211 | 0.13100 |
SWB(5) | 12 | 1.43618 | 1.97359 | 1.32007 | 0.04433 | 0.07602 |
SWB(5) | 20 | 1.43469 | 1.97223 | 1.31634 | 0.03927 | 0.07765 |
SWB(5) | 32 | 1.43463 | 1.97225 | 1.31607 | 0.03597 | 0.07765 |
RRG(2) | 10 | 1.55934 | 1.77122 | 1.41900 | 0.15869 | 0.32044 |
RRG(2) | 20 | 1.60061 | 1.76297 | 1.45744 | 0.16195 | 0.33977 |
RRG(2) | 30 | 1.61251 | 1.75289 | 1.46125 | 0.16997 | 0.35053 |
RRG(3) | 10 | 1.49614 | 1.87903 | 1.30837 | 0.17514 | 0.21708 |
RRG(3) | 20 | 1.52503 | 1.87847 | 1.37793 | 0.20373 | 0.22357 |
RRG(3) | 30 | 1.54129 | 1.87706 | 1.41134 | 0.21442 | 0.22868 |
RRG(4) | 10 | 1.44023 | 1.93770 | 1.30201 | 0.11648 | 0.13463 |
RRG(4) | 20 | 1.48205 | 1.93399 | 1.36490 | 0.14077 | 0.14659 |
RRG(4) | 30 | 1.48439 | 1.93797 | 1.37705 | 0.13959 | 0.14166 |
RRG(5) | 10 | 1.41641 | 1.95111 | 1.27098 | 0.10038 | 0.11042 |
RRG(5) | 20 | 1.42488 | 1.96513 | 1.30706 | 0.08722 | 0.08896 |
RRG(5) | 30 | 1.43068 | 1.96825 | 1.31653 | 0.08344 | 0.08393 |
SW(3) | 10 | 1.55356 | 1.87107 | 1.43216 | 0.16610 | 0.23788 |
SW(3) | 20 | 1.55998 | 1.86334 | 1.43951 | 0.22050 | 0.24702 |
SW(3) | 30 | 1.54842 | 1.88077 | 1.43167 | 0.21643 | 0.22839 |
SW(4) | 10 | 1.47637 | 1.91449 | 1.33514 | 0.14321 | 0.16987 |
SW(4) | 20 | 1.49157 | 1.93385 | 1.38141 | 0.14235 | 0.14885 |
SW(4) | 30 | 1.49811 | 1.93505 | 1.39764 | 0.14519 | 0.14804 |
SW(5) | 10 | 1.43017 | 1.95045 | 1.29919 | 0.09802 | 0.11240 |
SW(5) | 20 | 1.44575 | 1.95995 | 1.33955 | 0.09722 | 0.09962 |
SW(5) | 30 | 1.45251 | 1.96562 | 1.35962 | 0.08951 | 0.09047 |
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Baxter, G.J.; da Costa, R.A.; Dorogovtsev, S.N.; Mendes, J.F.F. Filtering Statistics on Networks. Entropy 2020, 22, 1149. https://doi.org/10.3390/e22101149
Baxter GJ, da Costa RA, Dorogovtsev SN, Mendes JFF. Filtering Statistics on Networks. Entropy. 2020; 22(10):1149. https://doi.org/10.3390/e22101149
Chicago/Turabian StyleBaxter, G. J., R. A. da Costa, S. N. Dorogovtsev, and J. F. F. Mendes. 2020. "Filtering Statistics on Networks" Entropy 22, no. 10: 1149. https://doi.org/10.3390/e22101149