228,972 research outputs found
Growing Scale-Free Networks with Tunable Clustering
We extend the standard scale-free network model to include a ``triad
formation step''. We analyze the geometric properties of networks generated by
this algorithm both analytically and by numerical calculations, and find that
our model possesses the same characteristics as the standard scale-free
networks like the power-law degree distribution and the small average geodesic
length, but with the high-clustering at the same time. In our model, the
clustering coefficient is also shown to be tunable simply by changing a control
parameter - the average number of triad formation trials per time step.Comment: Accepted for publication in Phys. Rev.
Growing Scale-free Small-world Networks with Tunable Assortative Coefficient
In this paper, we propose a simple rule that generates scale-free small-world
networks with tunable assortative coefficient. These networks are constructed
by two-stage adding process for each new node. The model can reproduce
scale-free degree distributions and small-world effect. The simulation results
are consistent with the theoretical predictions approximately. Interestingly,
we obtain the nontrivial clustering coefficient and tunable degree
assortativity by adjusting the parameter: the preferential exponent
. The model can unify the characterization of both assortative and
disassortative networks.Comment: 13 pages, and 5 figure
A general model for collaboration networks
In this paper, we propose a general model for collaboration networks.
Depending on a single free parameter "{\bf preferential exponent}", this model
interpolates between networks with a scale-free and an exponential degree
distribution. The degree distribution in the present networks can be roughly
classified into four patterns, all of which are observed in empirical data. And
this model exhibits small-world effect, which means the corresponding networks
are of very short average distance and highly large clustering coefficient.
More interesting, we find a peak distribution of act-size from empirical data
which has not been emphasized before of some collaboration networks. Our model
can produce the peak act-size distribution naturally that agrees with the
empirical data well.Comment: 10 pages, 10 figure
Scale-free networks with a large- to hypersmall-world transition
Recently there have been a tremendous interest in models of networks with a
power-law distribution of degree -- so called "scale-free networks." It has
been observed that such networks, normally, have extremely short path-lengths,
scaling logarithmically or slower with system size. As en exotic and
unintuitive example we propose a simple stochastic model capable of generating
scale-free networks with linearly scaling distances. Furthermore, by tuning a
parameter the model undergoes a phase transition to a regime with extremely
short average distances, apparently slower than log log N (which we call a
hypersmall-world regime). We characterize the degree-degree correlation and
clustering properties of this class of networks.Comment: errors fixed, one new figure, to appear in Physica
The Fractional Preferential Attachment Scale-Free Network Model
Many networks generated by nature have two generic properties: they are
formed in the process of {preferential attachment} and they are scale-free.
Considering these features, by interfering with mechanism of the {preferential
attachment}, we propose a generalisation of the Barab\'asi--Albert model---the
'Fractional Preferential Attachment' (FPA) scale-free network model---that
generates networks with time-independent degree distributions with degree exponent (where corresponds
to the typical value of the BA model). In the FPA model, the element
controlling the network properties is the parameter, where . Depending on the different values of parameter, we study the
statistical properties of the numerically generated networks. We investigate
the topological properties of FPA networks such as degree distribution, degree
correlation (network assortativity), clustering coefficient, average node
degree, network diameter, average shortest path length and features of
fractality. We compare the obtained values with the results for various
synthetic and real-world networks. It is found that, depending on , the FPA
model generates networks with parameters similar to the real-world networks.
Furthermore, it is shown that parameter has a significant impact on, among
others, degree distribution and degree correlation of generated networks.
Therefore, the FPA scale-free network model can be an interesting alternative
to existing network models. In addition, it turns out that, regardless of the
value of , FPA networks are not fractal.Comment: 16 pages, 6 figure
A Mutual Attraction Model for Both Assortative and Disassortative Weighted Networks
In most networks, the connection between a pair of nodes is the result of
their mutual affinity and attachment. In this letter, we will propose a Mutual
Attraction Model to characterize weighted evolving networks. By introducing the
initial attractiveness and the general mechanism of mutual attraction
(controlled by parameter ), the model can naturally reproduce scale-free
distributions of degree, weight and strength, as found in many real systems.
Simulation results are in consistent with theoretical predictions.
Interestingly, we also obtain nontrivial clustering coefficient C and tunable
degree assortativity r, depending on and A. Our weighted model appears as
the first one that unifies the characterization of both assortative and
disassortative weighted networks.Comment: 4 pages, 3 figure
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