Given that surprisingly little is known about the demography of human kinship, we provide a demographic account of the kinship networks of individuals in Sweden in 2017 across sex and cohort between ages 0 and 102. We used administrative register data of the full population of Sweden to provide the first kinship enumeration for a complete population based on empirical data. We created ego-focused kinship networks of children, parents, siblings, grandchildren, grandparents, aunts and uncles, nieces and nephews, and cousins. We show the average number of kin of different types, the distribution of the number of kin, and changes in dispersion over time. A large share of all kin of an individual are horizontal kin, such as cousins. We observe the highest number of kin—on average, roughly 20—around age 35. We show differences between matrilineal and patrilineal kin and differences in the kinship structure arising from fertility with more than one childbearing partner, such as half-siblings. The results demonstrate substantial variability in kinship within a population. We discuss our findings in the context of other methods to estimate kinship.