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Abstract
Bonacich (1987) suggested a family of centrality measures that provide a useful way of modeling questions of power and network constraint. However, the literature offers little guidance regarding the choice of β, the parameter which alters the way the measure accounts for the effect of having powerful contacts in ones network. In this paper I explore the way the choice of the β parameter affects the power indices the Bonacich measure generates. I consider three network properties which might affect the way the choice of β influences the Bonacich power indices. I find that in high density networks with few internal 'chains' and few pendants, the choice of β is largely immaterial. Conversely, in sparse networks, those with a high proportion of pendant nodes, or those with many chains, the value of β has a substantial effect on the power indices the measure generates. Next I consider whether power indices produced by interior values of β might be represented as a linear combination of "pure" vectors, those generated with values of β at either end of the parameter range and β = 0. I find that in the vast majority of cases a linear combination of "pure" vectors power is equivalent to using indices produced by interior values of β, making the choice of β largely moot. Finally, in the unlikely case that this disaggregation is inappropriate, I discuss the question of determining an appropriate value of β empirically.

Prior work has proposed different theoretical mechanisms to explain students' course-taking patterns in schools. On the one hand, there are oversocialized accounts that claim that rules, social background factors, and supply-side factors shape observed career patterns. On the other hand, there are undersocialized accounts that claim that the decisions of strategic agents and demand-side dynamics shape course-taking careers. In this article, the authors use simulations to illustrate how these theoretical mechanisms can generate course-taking patterns. Grounding the simulations in empirical data on the mathematics course taking of students in two high schools, they assess the relative merits of these competing theories by testing how closely observed and predicted career patterns align. The results reveal that the characteristics of students and the organizational rules and requirements of course-taking career systems render certain allocation mechanisms more salient than others. In particular, highly competitive and structurally constrained systems are shaped by supply dynamics, while less regulated systems of diverse populations are shaped by agent-based decision making.