Don't be dense now

The density is defined as $\frac{2e}{v(v-1)}$ where $v,e$ are the number of vertices and edges respectively. By simply doing a text replacement, we can count that there are 1890 0 s and 610 1 s.

• 610 1 s means there are 305 edges, so $e = 305$ .
• 1890 0 s and 610 1 s mean 2500 numbers in total. Since this is exactly the number of entries of a square matrix (the adjacency matrix is always square), the matrix is $50 \times 50$ . Thus, there are 50 vertices in total, or $v = 50$ .

Plugging the values in gives the answer immediately, $\frac{61}{245} \approx 0.2489$ .

This is not even a graph theory problem, just a string problem.