Step 1: Recall the classes of dienes.
Conjugated dienes have their two double bonds separated by exactly one single bond \((C=C-C=C)\); isolated dienes have two or more single bonds between them; cumulated dienes share a carbon \((C=C=C)\).
Step 2: Examine hepta-1,6-diene.
\(CH_2=CH-CH_2-CH_2-CH_2-CH=CH_2\): the double bonds are far apart (four single bonds), so it is isolated.
Step 3: Examine hepta-1,3-diene.
\(CH_2=CH-CH=CH-CH_2-CH_2-CH_3\): the double bonds are separated by just one single bond, the \(C=C-C=C\) pattern, so it is conjugated.
Step 4: Examine hepta-1,4-diene.
\(CH_2=CH-CH_2-CH=CH-CH_2-CH_3\): two single bonds separate the double bonds, so it is isolated.
Step 5: Examine hepta-1,5-diene.
\(CH_2=CH-CH_2-CH_2-CH=CH-CH_3\): again more than one single bond between the double bonds, so it is isolated.
Step 6: Conclude.
Only hepta-1,3-diene shows the conjugated arrangement.
\[ \boxed{\text{hepta-1,3-diene}} \]