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Convexity in complex networks
In: Network science, Volume 6, Issue 2, p. 176-203
ISSN: 2050-1250
AbstractMetric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration graphs due to their tree-like or clique-like structure, whereas the food web is the only network studied that is truly non-convex. Core–periphery networks are regionally convex as they can be divided into a non-convex core surrounded by a convex periphery. Random graphs, however, are only locally convex meaning that any connected subgraph of size smaller than the average geodesic distance between the nodes is almost certainly convex. We present different measures of network convexity and discuss its applications in the study of networks.
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Life Insurance Convexity
In: Proceedings of Paris December 2020 Finance Meeting EUROFIDAI - ESSEC
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Convexity, Risk, and Returns
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Schur convexity, quasi-convexity and preference for early resolution of uncertainty
In: Theory and decision: an international journal for multidisciplinary advances in decision science, Volume 39, Issue 2, p. 213-218
ISSN: 1573-7187
Theory of Generalized Convexity
In: Studies in Economic Theory; Multidimensional Screening, p. 51-60
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Topology of directional convexity
In: Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, Volume 56, Issue 4, p. 408-410
ISSN: 2524-2415
Herein, we have proven a Fink – Wood conjecture that if Oʹ is the closure of some orientation set O, then a set is a directed O-halfspace if and only if it is a directed Oʹ-halfspace.
S-Convexity and Gross Substitutability
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Hidden Convexity in Partially Separable Optimization
In: CentER Working Paper Series No. 2011-070
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