The persistent homology of genealogical networks

Applied Network Science

Table 1 The persistence intervals of the Tikopia genealogical network and the hexagon network are shown

Dimension	Interval Type and Persistence
Dimension	Tikopia	Hexagon
Dimension 0	\([0,\infty )\times 8, \ [0,1)\times 286\)	\([0,\infty )\times 1, \ [0,1)\times 1\)
Dimension 1	\([1,2)\times 16\), \([1,3)\times 19\), \([1,4)\times 5\), \([1,5)\times 3\), \([1,6)\times 2\), \([1,7)\times 1\)	\([1,2)\times 1\)
Dimension 2	\([2,3)\times 4\), \([3,4)\times 11\), \([4,5)\times 12\), \([5,6)\times 4\), \([6,7)\times 5\), \([7,8)\times 1\), \([8,9)\times 1\)	\([2,3)\times 1\)

Here the notation \([a,b)\times k\) indicates that the network has k persistence intervals [a, b). The corresponding persistence diagrams are shown in Fig. 6 and the corresponding persistence curve for the Tikopia network is shown in Fig. 7