The book is called Consequential Strangers: The Power of People Who Don't Seem to Matter But Really Do and is by Melina Blau and Karen L. Fingerman.
David Bollier reviews the book: "Consequential Strangers aggregates a diverse sociological literature to show just how valuable our casual social contacts truly are. For example, studies show that people with a rich web of relationships are less likely to come down with colds - presumably because it strengthens our immune system. People who lack close community ties are more likely to die nine years earlier than those with more extensive social connections. For women, it's 2.8 times more likely; for men, 2.3 times more likely. We are nurtured and fortified by our social connections, however casual."