Question: Can ImportGraph read a specified range of lines from a file?

We can read all the graphs in a file at once, or we can use an iterative approach. But can I specify a certain number of lines to read? 

with(GraphTheory):
g:=ImportGraph("E:/5cc3free.txt", graph6, output=list)

The contents of 5cc3free.txt are as follows (all 5-vertex C_3 free connected graphs).  There are 6 lines.

D?{
D@s
DBw
DFw
DDW
DqK

The reason for wanting this kind of operation is that sometimes there are tens of thousands of graphs stored in a single file, and I want to read them in batches. For example, I want to extract the graph data from lines 1-2, 3-4, and 5-6 in batches. How can I accomplish this?

In the previous example, a small dataset was used for demonstration purposes. In the following example, which involves all 8-vertex connected graphs (see the attachment graph8c.txt), I want to extract the graphs from lines 200-300. 

I found that readline always starts reading from the first line of a file, so the efficiency may not be very high.