The sample size for social network analysis (SNA) of ego-networks actually depends on the specific research question and the characteristics of the population. However, here are some general guidelines that you can follow.
Degree centrality is a measure of the number of connections an individual has in their ego network. A larger sample size will generally provide more accurate estimates of degree centrality. However, even small samples can be informative, especially if the network is relatively sparse.
Average tie strength is a measure of the average strength of the connections in an individual's ego network. This can be a more subjective measure than degree centrality, as it depends on how strength is defined. However, a larger sample size will generally provide more reliable estimates of average tie strength.
Effectiveness is a measure of the extent to which an individual can reach other members of their ego network through their connections. This is a more complex measure than degree centrality or average tie strength, and there is no single agreed-upon method for calculating it. However, a larger sample size will generally provide more accurate estimates of effectiveness.
Ego-betweenness is a measure of the extent to which an individual acts as a broker or connector in their ego network. This is a measure of the individual's structural importance. A larger sample size will generally provide more accurate estimates of ego-betweenness.
In general, a sample size of 50-100 ego networks is a good starting point for most SNA studies. However, if the network is particularly large or complex, a larger sample size may be necessary.
Here are some additional guidelines for determining the sample size for SNA of ego-networks:
Consider the variability of the network. If the network is very homogeneous, a smaller sample size may be sufficient. However, if the network is very heterogeneous, a larger sample size will be needed.
Consider the precision of the estimates. If you need very precise estimates of ego centrality, average tie strength, effectiveness, or ego-betweenness, you will need a larger sample size.
Consider the availability of data. If data on ego networks is difficult to collect, you may need to use a smaller sample size.