We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ∝ k −λ , i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ∼ ln N , we show, using analytical arguments, that scale free networks with 2 < λ < 3 have a much smaller diameter, behaving as d ∼ ln ln N . For λ = 3, our analysis yields d ∼ ln N/ ln ln N , as obtained by Bollobas and Riordan, while for λ > 3, d ∼ ln N . We also show that, for any λ > 2, one can construct a deterministic scale free network with d ∼ ln ln N , and this construction yields the lowest possible diameter.

Religious Zionists have been the driving force behind the settlement project in Israel for the past 40 years. They often see settling in the Greater Land of Israel as a messianic activity. It might be thought that when state policy clashes with radical messianic movements, the result would be violent, bloody confrontations. This study seeks to explain why this has not been the case in Israel despite the dismantling of settlements in the Sinai and Gaza and the controversial Oslo process. Although there has been turmoil and resistance, most religious Zionists have refrained from serious violence. We suggest that a “theological-normative balance” prevents all-out de-legitimation of the state and life-threatening violence against it.

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