345,680 research outputs found
Maximizing the Total Resolution of Graphs
A major factor affecting the readability of a graph drawing is its
resolution. In the graph drawing literature, the resolution of a drawing is
either measured based on the angles formed by consecutive edges incident to a
common node (angular resolution) or by the angles formed at edge crossings
(crossing resolution). In this paper, we evaluate both by introducing the
notion of "total resolution", that is, the minimum of the angular and crossing
resolution. To the best of our knowledge, this is the first time where the
problem of maximizing the total resolution of a drawing is studied.
The main contribution of the paper consists of drawings of asymptotically
optimal total resolution for complete graphs (circular drawings) and for
complete bipartite graphs (2-layered drawings). In addition, we present and
experimentally evaluate a force-directed based algorithm that constructs
drawings of large total resolution
Resolution of ranking hierarchies in directed networks
Identifying hierarchies and rankings of nodes in directed graphs is
fundamental in many applications such as social network analysis, biology,
economics, and finance. A recently proposed method identifies the hierarchy by
finding the ordered partition of nodes which minimises a score function, termed
agony. This function penalises the links violating the hierarchy in a way
depending on the strength of the violation. To investigate the resolution of
ranking hierarchies we introduce an ensemble of random graphs, the Ranked
Stochastic Block Model. We find that agony may fail to identify hierarchies
when the structure is not strong enough and the size of the classes is small
with respect to the whole network. We analytically characterise the resolution
threshold and we show that an iterated version of agony can partly overcome
this resolution limit.Comment: 27 pages, 9 figure
Optimal 3D Angular Resolution for Low-Degree Graphs
We show that every graph of maximum degree three can be drawn in three
dimensions with at most two bends per edge, and with 120-degree angles between
any two edge segments meeting at a vertex or a bend. We show that every graph
of maximum degree four can be drawn in three dimensions with at most three
bends per edge, and with 109.5-degree angles, i.e., the angular resolution of
the diamond lattice, between any two edge segments meeting at a vertex or bend.Comment: 18 pages, 10 figures. Extended version of paper to appear in Proc.
18th Int. Symp. Graph Drawing, Konstanz, Germany, 201
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