12,976 research outputs found
On the limiting behavior of parameter-dependent network centrality measures
We consider a broad class of walk-based, parameterized node centrality
measures for network analysis. These measures are expressed in terms of
functions of the adjacency matrix and generalize various well-known centrality
indices, including Katz and subgraph centrality. We show that the parameter can
be "tuned" to interpolate between degree and eigenvector centrality, which
appear as limiting cases. Our analysis helps explain certain correlations often
observed between the rankings obtained using different centrality measures, and
provides some guidance for the tuning of parameters. We also highlight the
roles played by the spectral gap of the adjacency matrix and by the number of
triangles in the network. Our analysis covers both undirected and directed
networks, including weighted ones. A brief discussion of PageRank is also
given.Comment: First 22 pages are the paper, pages 22-38 are the supplementary
material
Item weighted Kemeny distance for preference data
Preference data represent a particular type of ranking data where a group of people gives their preferences over a set of alternatives. The traditional metrics between rankings don’t take into account that the importance of elements can be not uniform. In this paper the item weighted Kemeny distance is introduced and its properties demonstrated
Egalitarianism in the rank aggregation problem: a new dimension for democracy
Winner selection by majority, in an election between two candidates, is the
only rule compatible with democratic principles. Instead, when the candidates
are three or more and the voters rank candidates in order of preference, there
are no univocal criteria for the selection of the winning (consensus) ranking
and the outcome is known to depend sensibly on the adopted rule. Building upon
XVIII century Condorcet theory, whose idea was to maximize total voter
satisfaction, we propose here the addition of a new basic principle (dimension)
to guide the selection: satisfaction should be distributed among voters as
equally as possible. With this new criterion we identify an optimal set of
rankings. They range from the Condorcet solution to the one which is the most
egalitarian with respect to the voters. We show that highly egalitarian
rankings have the important property to be more stable with respect to
fluctuations and that classical consensus rankings (Copeland, Tideman, Schulze)
often turn out to be non optimal. The new dimension we have introduced
provides, when used together with that of Condorcet, a clear classification of
all the possible rankings. By increasing awareness in selecting a consensus
ranking our method may lead to social choices which are more egalitarian
compared to those achieved by presently available voting systems.Comment: 18 pages, 14 page appendix, RateIt Web Tool:
http://www.sapienzaapps.it/rateit.php, RankIt Android mobile application:
https://play.google.com/store/apps/details?id=sapienza.informatica.rankit.
Appears in Quality & Quantity, 10 Apr 2015, Online Firs
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