So for each vertex \( v \), the number of paths of length 2 with center \( v \) is \( inom\deg(v)2 \), and each such path \( u-v-w \) uses edges \( uv \) and \( vw \), both in \( E \). Then the trio \( \u,v,w\ \) has exactly two close pairs (if no other edge), and since \( u \) and \( w \) are not necessarily connected, it’s exactly 2. - Veritas Home Health