22,852 research outputs found
Generating constrained random graphs using multiple edge switches
The generation of random graphs using edge swaps provides a reliable method
to draw uniformly random samples of sets of graphs respecting some simple
constraints, e.g. degree distributions. However, in general, it is not
necessarily possible to access all graphs obeying some given con- straints
through a classical switching procedure calling on pairs of edges. We therefore
propose to get round this issue by generalizing this classical approach through
the use of higher-order edge switches. This method, which we denote by "k-edge
switching", makes it possible to progres- sively improve the covered portion of
a set of constrained graphs, thereby providing an increasing, asymptotically
certain confidence on the statistical representativeness of the obtained
sample.Comment: 15 page
Evolving Clustered Random Networks
We propose a Markov chain simulation method to generate simple connected
random graphs with a specified degree sequence and level of clustering. The
networks generated by our algorithm are random in all other respects and can
thus serve as generic models for studying the impacts of degree distributions
and clustering on dynamical processes as well as null models for detecting
other structural properties in empirical networks
Multifractal Network Generator
We introduce a new approach to constructing networks with realistic features.
Our method, in spite of its conceptual simplicity (it has only two parameters)
is capable of generating a wide variety of network types with prescribed
statistical properties, e.g., with degree- or clustering coefficient
distributions of various, very different forms. In turn, these graphs can be
used to test hypotheses, or, as models of actual data. The method is based on a
mapping between suitably chosen singular measures defined on the unit square
and sparse infinite networks. Such a mapping has the great potential of
allowing for graph theoretical results for a variety of network topologies. The
main idea of our approach is to go to the infinite limit of the singular
measure and the size of the corresponding graph simultaneously. A very unique
feature of this construction is that the complexity of the generated network is
increasing with the size. We present analytic expressions derived from the
parameters of the -- to be iterated-- initial generating measure for such major
characteristics of graphs as their degree, clustering coefficient and
assortativity coefficient distributions. The optimal parameters of the
generating measure are determined from a simple simulated annealing process.
Thus, the present work provides a tool for researchers from a variety of fields
(such as biology, computer science, biology, or complex systems) enabling them
to create a versatile model of their network data.Comment: Preprint. Final version appeared in PNAS
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