Testing centralization in random graphs Export

@article{citeulike:3955208, abstract = {Centrality is an important concept in social network analysis which involves identification of important or prominent actors. Three common definitions of centrality are degree centrality, closeness centrality and betwenness centrality which yield actor indices. By aggregating these actor indices of centrality across actors, we obtain a single group-level index of centralization. In this paper, we consider the problem of testing whether the observed data is likely to have come from a particular kind of centralized structure of a given size, edge probability and extent of centralization. Eight different group-level indices of centralization are used as test statistics of graph centralization. As our graph model, we assume a general blockmodel which allows a rich probabilistic structure. By carrying out a simulation study the performance of the tests is evaluated by comparing their power functions. The results imply that two tests based on degree and four tests based on closeness have high power. In addition, critical values of the tests are modeled conditional on graph parameters via a linear regression model. An application is illustrated with analysis on a real data set.}, author = {Tallberg, C.}, citeulike-article-id = {3955208}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.socnet.2004.02.001}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0378-8733(04)00012-7}, doi = {10.1016/j.socnet.2004.02.001}, issn = {03788733}, journal = {Social Networks}, keywords = {bernoulli, betweenness, centralization, closeness, degree, graph, graph-theoretical, network, power-law, random, social-network, stochastic, variance}, month = {July}, number = {3}, pages = {205--219}, posted-at = {2009-01-26 19:25:16}, priority = {3}, title = {Testing centralization in random graphs}, url = {http://dx.doi.org/10.1016/j.socnet.2004.02.001}, volume = {26}, year = {2004} }

TY - JOUR ID - citeulike:3955208 L3 - citeulike-article-id:3955208 N2 - Centrality is an important concept in social network analysis which involves identification of important or prominent actors. Three common definitions of centrality are degree centrality, closeness centrality and betwenness centrality which yield actor indices. By aggregating these actor indices of centrality across actors, we obtain a single group-level index of centralization. In this paper, we consider the problem of testing whether the observed data is likely to have come from a particular kind of centralized structure of a given size, edge probability and extent of centralization. Eight different group-level indices of centralization are used as test statistics of graph centralization. As our graph model, we assume a general blockmodel which allows a rich probabilistic structure. By carrying out a simulation study the performance of the tests is evaluated by comparing their power functions. The results imply that two tests based on degree and four tests based on closeness have high power. In addition, critical values of the tests are modeled conditional on graph parameters via a linear regression model. An application is illustrated with analysis on a real data set. IS - 3 JF - Social Networks SN - 03788733 EP - 219 TI - Testing centralization in random graphs VL - 26 SP - 205 KW - bernoulli KW - betweenness KW - centralization KW - closeness KW - degree KW - graph KW - graph-theoretical KW - network KW - power-law KW - random KW - social-network KW - stochastic KW - variance AU - Tallberg, C PY - 2004/07// UR - http://dx.doi.org/10.1016/j.socnet.2004.02.001 ER -