@incollection{koschtzki2005centrality,
  abstract = {Centrality indices are to quantify an intuitive feeling that in most networks some vertices or edges are more central than others. Many vertex centrality indices were introduced for the first time in the 1950s: e.g., the Bavelas index [50, 51], degree centrality [483] or a first feedback centrality, introduced by Seeley [510]. These early centralities raised a rush of research in which manifold applications were found. However, not every centrality index was suitable to every application, so with time, dozens of new centrality indices were published. This chapter will present some of the more influential, ‘classic’ centrality indices. We do not strive for completeness, but hope to give a catalog of basic centrality indices with some of their main applications.},
  address = {Berlin / Heidelberg},
  affiliation = {IPK Gatersleben, Corrensstraße 3, 06466 Gatersleben, Germany},
  author = {Koschützki, Dirk and Lehmann, Katharina and Peeters, Leon and Richter, Stefan and Tenfelde-Podehl, Dagmar and Zlotowski, Oliver},
  booktitle = {Network Analysis},
  doi = {10.1007/978-3-540-31955-9_3},
  editor = {Brandes, Ulrik and Erlebach, Thomas},
  interhash = {8bfa60518049d9dbc7f6ce7b5c2914be},
  intrahash = {567d2f61b08e78af53463b2a30729830},
  isbn = {978-3-540-24979-5},
  keyword = {Computer Science},
  pages = {16-61},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Centrality Indices},
  url = {http://dx.doi.org/10.1007/978-3-540-31955-9_3},
  volume = 3418,
  year = 2005
}

@book{brandes2005network,
  address = {[New York]},
  author = {Brandes, Ulrik. and Erlebach, Thomas.},
  interhash = {ae40403faa9a80926c66da73cf6e29ba},
  intrahash = {11695c81746f2ac6e25fab7c6ed49fbf},
  isbn = {9783540249795 3540249796 9783540319559 3540319557},
  publisher = {Springer-Verlag Berlin/Heidelberg},
  refid = {318289062},
  title = {Network Analysis},
  url = {http://www.worldcat.org/search?qt=worldcat_org_all&q=3540249796},
  year = 2005
}

@misc{newman2003measure,
  abstract = {Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks.},
  archiveprefix = {arXiv},
  author = {Newman, M. E. J.},
  citeulike-article-id = {79840},
  citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0309045},
  citeulike-linkout-1 = {http://arxiv.org/pdf/cond-mat/0309045},
  eprint = {cond-mat/0309045},
  interhash = {cf0943b7e57fd12b3489da4224bd5513},
  intrahash = {50120fee4be9343e5a5d9cfa7d4b3a9e},
  month = {September},
  posted-at = {2006-05-02 14:16:40},
  priority = {4},
  title = {A measure of betweenness centrality based on random walks},
  url = {http://arxiv.org/abs/cond-mat/0309045},
  year = 2003
}