310,181 research outputs found
The group of causal automorphisms
The group of causal automorphisms on Minkowski space-time is given and its
structure is analyzed
The q-component static model : modeling social networks
We generalize the static model by assigning a q-component weight on each
vertex. We first choose a component among the q components at random
and a pair of vertices is linked with a color according to their weights
of the component as in the static model. A (1-f) fraction of the entire
edges is connected following this way. The remaining fraction f is added with
(q+1)-th color as in the static model but using the maximum weights among the q
components each individual has. This model is motivated by social networks. It
exhibits similar topological features to real social networks in that: (i) the
degree distribution has a highly skewed form, (ii) the diameter is as small as
and (iii) the assortativity coefficient r is as positive and large as those in
real social networks with r reaching a maximum around .Comment: 5 pages, 6 figure
Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture
We introduce a new combinatorial abstraction for the graphs of polyhedra. The
new abstraction is a flexible framework defined by combinatorial properties,
with each collection of properties taken providing a variant for studying the
diameters of polyhedral graphs. One particular variant has a diameter which
satisfies the best known upper bound on the diameters of polyhedra. Another
variant has superlinear asymptotic diameter, and together with some
combinatorial operations, gives a concrete approach for disproving the Linear
Hirsch Conjecture.Comment: 16 pages, 4 figure
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