Delinquent Networks

Key leaders in social networks

“…They demonstrate that construction of the Nash equilibrium uses "weighted Katz-Bonacich Centrality," establishing a connection between the network economics literature and the sociology literature. Ballester et al [5] extend the idea of identifying the key player in Ballester et al [3] along two dimensions: the optimal policies for removal of a group of players (a key group) and removal of one link (a key link). Liu et al [16] allow the remaining players to form new links after a player is removed.…”

“…They assume {α i }'s are homogeneous and are normalized to 1 (see Liu et al [16] for the heterogeneous case). To illustrate the difference between the intercentrality measure and the L-index, we revisit a regular graph studied in Ballester et al [5] and Calvo-Armengol and Jackson [8]. As illustrated in Fig.…”

“…The calculations in Table 1 show that player 3 is the key leader, whereas player 1 is the key player. 5 5 More generally, when all {b i }'s are the same, 1 ≤ m jj < m ii < 2. It is easy to see that c i < c j but L i > L j .…”

Key Player Policies When Contextual Effects Matter

“…However, in their model, contextual effects are not taken into account; that is, only each individual's characteristics affect her effort but not the characteristics of her friends. In the present article, we extend this intercentrality measure to include contextual effects and show that the formula proposed by Ballester et al (2006Ballester et al ( , 2010 must be adapted to a more general case.…”

“…As a result, criminal behaviors can be magnified and interventions can become more effective. Based on a peer effect model, Ballester et al (2006Ballester et al ( , 2010 have proposed a centrality measure (the intercentrality measure) that determines the key player in each network. However, in their model, contextual effects are not taken into account; that is, only each individual's characteristics affect her effort but not the characteristics of her friends.…”