Detecting households is not the same as detecting communities!
In applied graph analytics, the first cluster is often not the real unit you care about.
The Problem
In a family-detection project, I started from precomputed communication communities (SAS CLA results). The algorithm found groups of people who call each other.
A communication community is not necessarily a household. A single community can contain extended family spread across the city, multiple separate households, and close friends who call frequently.
I needed to separate two distinct levels of social structure:
The big family
The broader connected social unit (20-30 people)
The household / foyer
The smaller co-living unit (4-6 people)
Two Signals
Signal 1: Communication intensity (with ranking)
Not just 'how many calls?' but who ranks highest. Top 5 outgoing + top 5 incoming contacts, weighted by position (1st = 5 points, 2nd = 4, etc.). Household members consistently appear in each other's top tier.
Signal 2: Shared location behavior (cell tower dominance)
Which cell tower shows up most in your evening CDR? The dominant evening tower = home location. People spend ~8 hours a night in the same place. Two people in the same household share a dominant evening tower with very high probability.
The Rule
Same community + top-ranked contact + shared evening tower = household tie.
The algorithm found the network. The refinement found the household.
Key Takeaway
Design insight: In applied graph analytics, the first cluster is often not the real unit you care about. Graph membership alone is not enough — combine it with behavioral signals to find the real structure.