**Problem1H: A graph on the vertex set **** is often descried by a matrix **** of size **** where **** and **** are equal to the number of edges with ends **** and ****. What is the combinatorial interpretation of the entries of the matrix ****?**

**Solution:** Let then easy to see that means the number of walks of length from vertex to vertiex

**Note:** Let then means the number of walks of length from to The edge can be repeated, thus we use ‘walk’ instead of ‘path’. How can we find the number of paths of length from vertex to vertex ?