372 research outputs found
Subgraphs in preferential attachment models
We consider subgraph counts in general preferential attachment models with
power-law degree exponent . For all subgraphs , we find the scaling
of the expected number of subgraphs as a power of the number of vertices. We
prove our results on the expected number of subgraphs by defining an
optimization problem that finds the optimal subgraph structure in terms of the
indices of the vertices that together span it and by using the representation
of the preferential attachment model as a P\'olya urn model
Degree correlations in scale-free null models
We study the average nearest neighbor degree of vertices with degree
. In many real-world networks with power-law degree distribution
falls off in , a property ascribed to the constraint that any two vertices
are connected by at most one edge. We show that indeed decays in in
three simple random graph null models with power-law degrees: the erased
configuration model, the rank-1 inhomogeneous random graph and the hyperbolic
random graph. We consider the large-network limit when the number of nodes
tends to infinity. We find for all three null models that starts to
decay beyond and then settles on a power law , with the degree exponent.Comment: 21 pages, 4 figure
Predicting the long-term citation impact of recent publications
A fundamental problem in citation analysis is the prediction of the long-term
citation impact of recent publications. We propose a model to predict a
probability distribution for the future number of citations of a publication.
Two predictors are used: The impact factor of the journal in which a
publication has appeared and the number of citations a publication has received
one year after its appearance. The proposed model is based on quantile
regression. We employ the model to predict the future number of citations of a
large set of publications in the field of physics. Our analysis shows that both
predictors (i.e., impact factor and early citations) contribute to the accurate
prediction of long-term citation impact. We also analytically study the
behavior of the quantile regression coefficients for high quantiles of the
distribution of citations. This is done by linking the quantile regression
approach to a quantile estimation technique from extreme value theory. Our work
provides insight into the influence of the impact factor and early citations on
the long-term citation impact of a publication, and it takes a step toward a
methodology that can be used to assess research institutions based on their
most recently published work.Comment: 17 pages, 17 figure
Networks with communities and clustering
Groepen binnen netwerken zorgen soms toch voor snellere verspreidin
Switch chain mixing times through triangle counts
Sampling uniform simple graphs with power-law degree distributions with
degree exponent is a non-trivial problem. We propose a method to
sample uniform simple graphs that uses a constrained version of the
configuration model together with a Markov Chain switching method. We test the
convergence of this algorithm numerically in the context of the presence of
small subgraphs. We then compare the number of triangles in uniform random
graphs with the number of triangles in the erased configuration model. Using
simulations and heuristic arguments, we conjecture that the number of triangles
in the erased configuration model is larger than the number of triangles in the
uniform random graph, provided that the graph is sufficiently large.Comment: 7 pages, 8 figures in the main article. 2 pages, 2 figures in the
supplementary materia
Degree correlations in scale-free null models
We study the average nearest neighbor degree of vertices with degree . In many real-world networks with power-law degree distribution falls off in , a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that indeed decays in in three simple random graph null models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph and the hyperbolic random graph. We consider the large-network limit when the number of nodes tends to infinity. We find for all three null models that starts to decay beyond and then settles on a power law , with the degree exponent
Variational principle for scale-free network motifs
For scale-free networks with degrees following a power law with an exponent
, the structures of motifs (small subgraphs) are not yet well
understood. We introduce a method designed to identify the dominant structure
of any given motif as the solution of an optimization problem. The unique
optimizer describes the degrees of the vertices that together span the most
likely motif, resulting in explicit asymptotic formulas for the motif count and
its fluctuations. We then classify all motifs into two categories: motifs with
small and large fluctuations
Closure coefficients in scale-free complex networks
The formation of triangles in complex networks is an important network
property that has received tremendous attention. The formation of triangles is
often studied through the clustering coefficient. The closure coefficient or
transitivity is another method to measure triadic closure. This statistic
measures clustering from the head node of a triangle (instead of from the
center node, as in the often studied clustering coefficient). We perform a
first exploratory analysis of the behavior of the local closure coefficient in
two random graph models that create simple networks with power-law degrees: the
hidden-variable model and the hyperbolic random graph. We show that the closure
coefficient behaves significantly different in these simple random graph models
than in the previously studied multigraph models. We also relate the closure
coefficient of high-degree vertices to the clustering coefficient and the
average nearest neighbor degree
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