A min-cost/max flow formulation for the s-metric normalisation on directed graphs
A min-cost/max flow formulation for the s-metric normalisation on directed graphs
In the literature of scale-free graphs, the s-Metric (S(G)) aims at quantifying the extent at which a connected, undirected graph G(V;E) is scale free [1]. Moreover, S(G) measures the extent at which G has a hub-like core and is maximized/minimised when high-degree nodes are connected
to high/low degree nodes. Among the family of graphs F(D), which exhibit identical degree sequence, the graph Gmax/Gmin has the maximum/minimum s-Metric, and thus it can be used for the normalisation of the S(G) for every G 2 F(D) [1]. We show that for a given digraph G(V;E), the graph Gmax=Gmin can be derived in polynomial time.
Kaparis, Konstantinos
29a564bc-2835-43ee-bf21-50e65e0a894a
Fliege, Joerg
54978787-a271-4f70-8494-3c701c893d98
Kaparis, Konstantinos
29a564bc-2835-43ee-bf21-50e65e0a894a
Fliege, Joerg
54978787-a271-4f70-8494-3c701c893d98
Kaparis, Konstantinos and Fliege, Joerg
(2010)
A min-cost/max flow formulation for the s-metric normalisation on directed graphs
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Abstract
In the literature of scale-free graphs, the s-Metric (S(G)) aims at quantifying the extent at which a connected, undirected graph G(V;E) is scale free [1]. Moreover, S(G) measures the extent at which G has a hub-like core and is maximized/minimised when high-degree nodes are connected
to high/low degree nodes. Among the family of graphs F(D), which exhibit identical degree sequence, the graph Gmax/Gmin has the maximum/minimum s-Metric, and thus it can be used for the normalisation of the S(G) for every G 2 F(D) [1]. We show that for a given digraph G(V;E), the graph Gmax=Gmin can be derived in polynomial time.
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Submitted date: 2010
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Operational Research
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Local EPrints ID: 156275
URI: http://eprints.soton.ac.uk/id/eprint/156275
PURE UUID: 7de15ace-5cc6-4d4c-a7f7-dca9118d42d2
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Date deposited: 08 Jun 2010 13:13
Last modified: 12 Apr 2024 01:41
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Author:
Konstantinos Kaparis
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