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In this work we propose a centrality measure for networks, which we refer to as Laplacian centrality, that provides a general framework for the centrality of a vertex based on the idea that the importance (or centrality) of a vertex is related to the ability of the network to respond to the deactivation or removal of that vertex from the network. In particular, the Laplacian centrality of a vertex is defined as the relative drop of Laplacian energy caused by the deactivation of this vertex. The Laplacian energy of network with n vertices is defined as G is the eigenvalue of the Laplacian matrix of . Other dynamics-based measures such as that of Masuda and Kori and Pag-eRank compute the importance of a node by analyzing the way paths pass through a node while our measure captures this information as well as the way these paths are "redistributed" when the node is deleted. The validity and robustness of this new measure are illustrated on two different terrorist social network data sets and 84 networks in James Moody's Add Health in-school friendship nomination data, and is compared with other standard centrality measures. G

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A pre-test and post-test quasi-experimental matched pairs design was used to assess the effectiveness of a week-long multi-therapist intensive outpatient intervention process with clergy suffering from depression and burnout. Participants (n = 23) in the "Clergy in Kairos" program of the Pastoral Institute (Muse in J Pastor Care Couns 61(3):183-195, 2007) constituted the experimental variable. Clergy surveyed from United Methodist and Presbyterian denominations (n = 121) provided a control group from which 23 respondents were selected whose pre-test scores in depression and burnout were statistically equivalent to those in the experimental group. The treatment group consisted of clergy from three denominations who self-selected (or in some cases were referred by denominational officials) into the program. At the outset, clergy in both groups reported equivalent levels of conflict, emotional exhaustion, depersonalization, and depression. At the 6-months follow-up, clergy in the experimental group showed significant improvement of depression, emotional exhaustion, and depersonalization scores. By contrast, there was no change in the burnout and depression scores in the control group at 6-months post-test. Findings suggest the usefulness of a week-long multi-therapist intensive outpatient intervention in reducing burnout and depression.

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