80,091 research outputs found
Deterministic hierarchical networks
It has been shown that many networks associated with complex systems are
small-world (they have both a large local clustering coefficient and a small
diameter) and they are also scale-free (the degrees are distributed according
to a power law). Moreover, these networks are very often hierarchical, as they
describe the modularity of the systems that are modeled. Most of the studies
for complex networks are based on stochastic methods. However, a deterministic
method, with an exact determination of the main relevant parameters of the
networks, has proven useful. Indeed, this approach complements and enhances the
probabilistic and simulation techniques and, therefore, it provides a better
understanding of the systems modeled. In this paper we find the radius,
diameter, clustering coefficient and degree distribution of a generic family of
deterministic hierarchical small-world scale-free networks that has been
considered for modeling real-life complex systems
Deterministic hierarchical networks
It has been shown that many networks associated with complex systems are
small-world (they have both a large local clustering coefficient and a small
diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances
the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.Peer ReviewedPostprint (author's final draft
Deterministic hierarchical networks
Recently it has been shown that many networks associated with complex systems are small-world (they have both a large local
clustering and a small diameter) and they are also scale-free (the degrees are distributed according to a power-law). Moreover, these networks are very often hierarchical, as they describe the
modularity of the systems which are modeled. Most of the studies for complex networks are based on stochastic methods. However, a
deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation
techniques and, therefore, it provides a better understanding of the systems modeled.
In this paper we find the radius, diameter, clustering and degree distribution of a generic family of deterministic hierarchical
small-world scale-free networks which has been considered for modeling real life complex systems. Moreover a routing algorithm is proposed
Deterministic hierarchical networks
It has recently been shown that many networks associated
with complex systems are small-world (they have both a large local clustering
and a small average distance and diameter) and they are also
scale-free (the degrees are distributed according to a power-law).
Moreover, these networks are very often hierarchical, as they describe the
modularity of the systems which are modeled.
While most of the studies for complex networks are based on
stochastic methods,
a deterministic approach, with an exact determination
of the main relevant parameters of the networks, has proven useful
to complement and enhance the probabilistic and simulation techniques and
therefore to provide a better understanding of the systems modeled.
In this paper we find the diameter, clustering and degree
distribution of a generic family of deterministic hierarchical small-world scale-free
networks which has been considered for modeling real life complex systems
Average distance in a hierarchical scale-free network: an exact solution
Various real systems simultaneously exhibit scale-free and hierarchical
structure. In this paper, we study analytically average distance in a
deterministic scale-free network with hierarchical organization. Using a
recursive method based on the network construction, we determine explicitly the
average distance, obtaining an exact expression for it, which is confirmed by
extensive numerical calculations. The obtained rigorous solution shows that the
average distance grows logarithmically with the network order (number of nodes
in the network). We exhibit the similarity and dissimilarity in average
distance between the network under consideration and some previously studied
networks, including random networks and other deterministic networks. On the
basis of the comparison, we argue that the logarithmic scaling of average
distance with network order could be a generic feature of deterministic
scale-free networks.Comment: Definitive version published in Journal of Statistical Mechanic
Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
In this paper, firstly, we study analytically the topological features of a
family of hierarchical lattices (HLs) from the view point of complex networks.
We derive some basic properties of HLs controlled by a parameter . Our
results show that scale-free networks are not always small-world, and support
the conjecture that self-similar scale-free networks are not assortative.
Secondly, we define a deterministic family of graphs called small-world
hierarchical lattices (SWHLs). Our construction preserves the structure of
hierarchical lattices, while the small-world phenomenon arises. Finally, the
dynamical processes of intentional attacks and collective synchronization are
studied and the comparisons between HLs and Barab{\'asi}-Albert (BA) networks
as well as SWHLs are shown. We show that degree distribution of scale-free
networks does not suffice to characterize their synchronizability, and that
networks with smaller average path length are not always easier to synchronize.Comment: 26 pages, 8 figure
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