25,345 research outputs found
Characteristic exponents of complex networks
We present a novel way to characterize the structure of complex networks by
studying the statistical properties of the trajectories of random walks over
them. We consider time series corresponding to different properties of the
nodes visited by the walkers. We show that the analysis of the fluctuations of
these time series allows to define a set of characteristic exponents which
capture the local and global organization of a network. This approach provides
a way of solving two classical problems in network science, namely the
systematic classification of networks, and the identification of the salient
properties of growing networks. The results contribute to the construction of a
unifying framework for the investigation of the structure and dynamics of
complex systems.Comment: 6 pages, 5 figures, 1 tabl
Phase transitions with infinitely many absorbing states in complex networks
We instigate the properties of the threshold contact process (TCP), a process
showing an absorbing-state phase transition with infinitely many absorbing
states, on random complex networks. The finite size scaling exponents
characterizing the transition are obtained in a heterogeneous mean field (HMF)
approximation and compared with extensive simulations, particularly in the case
of heterogeneous scale-free networks. We observe that the TCP exhibits the same
critical properties as the contact process (CP), which undergoes an
absorbing-state phase transition to a single absorbing state. The accordance
among the critical exponents of different models and networks leads to
conjecture that the critical behavior of the contact process in a HMF theory is
a universal feature of absorbing state phase transitions in complex networks,
depending only on the locality of the interactions and independent of the
number of absorbing states. The conditions for the applicability of the
conjecture are discussed considering a parallel with the
susceptible-infected-susceptible epidemic spreading model, which in fact
belongs to a different universality class in complex networks.Comment: 9 pages, 6 figures to appear in Phys Rev
Triadic closure dynamics drives scaling-laws in social multiplex networks
Social networks exhibit scaling-laws for several structural characteristics,
such as the degree distribution, the scaling of the attachment kernel, and the
clustering coefficients as a function of node degree. A detailed understanding
if and how these scaling laws are inter-related is missing so far, let alone
whether they can be understood through a common, dynamical principle. We
propose a simple model for stationary network formation and show that the three
mentioned scaling relations follow as natural consequences of triadic closure.
The validity of the model is tested on multiplex data from a well studied
massive multiplayer online game. We find that the three scaling exponents
observed in the multiplex data for the friendship, communication and trading
networks can simultaneously be explained by the model. These results suggest
that triadic closure could be identified as one of the fundamental dynamical
principles in social multiplex network formation.Comment: 5 pages, 3 figure
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