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Subdivision Drawings of Hypergraphs
"... We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertexbased Venn diag ..."
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We introduce the concept of subdivision drawings of hypergraphs. In a subdivision drawing each vertex corresponds uniquely to a face of a planar subdivision and, for each hyperedge, the union of the faces corresponding to the vertices incident to that hyperedge is connected. Vertexbased Venn diagrams and concrete Euler diagrams are both subdivision drawings. In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertexbased Venn diagrams. They allow us to draw more hypergraphs than the former while having better aesthetic properties than the latter.
Blocks of Hypergraphs  applied to Hypergraphs and Outerplanarity
, 2010
"... A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is N Pcomplete to decide w ..."
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Cited by 4 (2 self)
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A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is N Pcomplete to decide whether a hypergraph has a 2outerplanar support, we show how to test in polynomial time whether a hypergraph that is closed under intersections and differences has an outerplanar or a planar support. In all cases our algorithms yield a construction of the required support if it exists. The algorithms are based on a new definition of biconnected components in hypergraphs.
Social Networks
, 2005
"... Social networks provide a rich source of graph drawing problems, because they appear in an incredibly wide variety of forms and contexts. After sketching the scope of social network analysis, we establish some general principles for social network visualization before finally reviewing applications ..."
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Cited by 1 (0 self)
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Social networks provide a rich source of graph drawing problems, because they appear in an incredibly wide variety of forms and contexts. After sketching the scope of social network analysis, we establish some general principles for social network visualization before finally reviewing applications of, and challenges for, graph drawing methods in this area. Other accounts more generally relating to social network visualization are given, e.g., in [Klo81, BKR + 99a, Fre00, Fre05, BKR06].
Overlapping Patterns Recognition with Linear and NonLinear Separations using Positive Definite Kernels
, 2012
"... 41 rue de la liberte, ..."
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