An alternate take on this from the title: like any industry, homeland security (for example) is likely to be a tightly knit cluster of people -- you generally network on LinkedIn (and in life) with people in your own industry.

Now at even two degrees away, a single tenuous connection from the author to this cluster would instantly put the bulk of that cluster into the author's "extended network", and lead to the scary visualization shown. This connection could literally be a recruiter connecting to two essentially random people. At higher degrees of separation, the probability of finding such a path increases dramatically, to the point of almost certainty.

In other words, don't use these so-called "extended networks" for any serious analysis, and don't always trust tree visualizations of social networks.