6 research outputs found
Explosive Percolation in the Human Protein Homology Network
We study the explosive character of the percolation transition in a
real-world network. We show that the emergence of a spanning cluster in the
Human Protein Homology Network (H-PHN) exhibits similar features to an
Achlioptas-type process and is markedly different from regular random
percolation. The underlying mechanism of this transition can be described by
slow-growing clusters that remain isolated until the later stages of the
process, when the addition of a small number of links leads to the rapid
interconnection of these modules into a giant cluster. Our results indicate
that the evolutionary-based process that shapes the topology of the H-PHN
through duplication-divergence events may occur in sudden steps, similarly to
what is seen in first-order phase transitions.Comment: 13 pages, 6 figure
Transition from fractal to non-fractal scalings in growing scale-free networks
Real networks can be classified into two categories: fractal networks and
non-fractal networks. Here we introduce a unifying model for the two types of
networks. Our model network is governed by a parameter . We obtain the
topological properties of the network including the degree distribution,
average path length, diameter, fractal dimensions, and betweenness centrality
distribution, which are controlled by parameter . Interestingly, we show
that by adjusting , the networks undergo a transition from fractal to
non-fractal scalings, and exhibit a crossover from `large' to small worlds at
the same time. Our research may shed some light on understanding the evolution
and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in
EPJ
Role of fractal dimension in random walks on scale-free networks
Fractal dimension is central to understanding dynamical processes occurring
on networks; however, the relation between fractal dimension and random walks
on fractal scale-free networks has been rarely addressed, despite the fact that
such networks are ubiquitous in real-life world. In this paper, we study the
trapping problem on two families of networks. The first is deterministic, often
called -flowers; the other is random, which is a combination of
-flower and -flower and thus called hybrid networks. The two
network families display rich behavior as observed in various real systems, as
well as some unique topological properties not shared by other networks. We
derive analytically the average trapping time for random walks on both the
-flowers and the hybrid networks with an immobile trap positioned at an
initial node, i.e., a hub node with the highest degree in the networks. Based
on these analytical formulae, we show how the average trapping time scales with
the network size. Comparing the obtained results, we further uncover that
fractal dimension plays a decisive role in the behavior of average trapping
time on fractal scale-free networks, i.e., the average trapping time decreases
with an increasing fractal dimension.Comment: Definitive version published in European Physical Journal