In many molecules the π systems are electronically separated from the σ networks. There is nothing surprising about it. The π systems are perpendicular to σ bonds (they do not overlap with each other), and the interactions between them are nonexistent or very small. There are exceptions of course (for example, see hyperconjugation), but this separation makes analysis of orbital systems, and especially identifying the HOMO and the LUMO, much easier.

Here are some examples. We forget here about all σ bonds and concentrate only on the π systems. These are built out of atomic p orbitals on carbons participating in the π bonding (one p orbital per carbon). We have grouped them in a big table: starting with a single p orbital as a reference. We show these orbitals from two points of view: from the side of the π system (the top of the table), and from above of the π networks (the bottom of the table). We have included here ethylene (two p orbitals), allyl system (three p orbitals), butadiene (four p orbitals) and benzene (six p orbitals in a cyclic arrangements).  The orbitals are arranged (approximately) according to their energy (note that the bottom part of the table is just a repetition of the top part). For each system the number of nodes increases together with the energy of the orbital. The relative sizes of the lobes are better appreciated in the view from the top (the bottom table).   Some of the individual molecules listed here are discussed in more detail in the Molecular Gallery and you can calculate MO of any π system using a simple Hückel algorithm.