22,517 research outputs found
Identity and Search in Social Networks
Social networks have the surprising property of being "searchable": Ordinary
people are capable of directing messages through their network of acquaintances
to reach a specific but distant target person in only a few steps. We present a
model that offers an explanation of social network searchability in terms of
recognizable personal identities: sets of characteristics measured along a
number of social dimensions. Our model defines a class of searchable networks
and a method for searching them that may be applicable to many network search
problems, including the location of data files in peer-to-peer networks, pages
on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte
Geographical Coarsegraining of Complex Networks
We perform the renormalization-group-like numerical analysis of
geographically embedded complex networks on the two-dimensional square lattice.
At each step of coarsegraining procedure, the four vertices on each square box are merged to a single vertex, resulting in the coarsegrained
system of the smaller sizes. Repetition of the process leads to the observation
that the coarsegraining procedure does not alter the qualitative
characteristics of the original scale-free network, which opens the possibility
of subtracting a smaller network from the original network without destroying
the important structural properties. The implication of the result is also
suggested in the context of the recent study of the human brain functional
network.Comment: To appear in Phys. Rev. Let
Dynamics of opinion formation in a small-world network
The dynamical process of opinion formation within a model using a local
majority opinion updating rule is studied numerically in networks with the
small-world geometrical property. The network is one in which shortcuts are
added to randomly chosen pairs of nodes in an underlying regular lattice. The
presence of a small number of shortcuts is found to shorten the time to reach a
consensus significantly. The effects of having shortcuts in a lattice of fixed
spatial dimension are shown to be analogous to that of increasing the spatial
dimension in regular lattices. The shortening of the consensus time is shown to
be related to the shortening of the mean shortest path as shortcuts are added.
Results can also be translated into that of the dynamics of a spin system in a
small-world network.Comment: 10 pages, 5 figure
Characterization and control of small-world networks
Recently Watts and Strogatz have given an interesting model of small-world
networks. Here we concretise the concept of a ``far away'' connection in a
network by defining a {\it far edge}. Our definition is algorithmic and
independent of underlying topology of the network. We show that it is possible
to control spread of an epidemic by using the knowledge of far edges. We also
suggest a model for better advertisement using the far edges. Our findings
indicate that the number of far edges can be a good intrinsic parameter to
characterize small-world phenomena.Comment: 9 pages and 6 figure
A novel approach to study realistic navigations on networks
We consider navigation or search schemes on networks which are realistic in
the sense that not all search chains can be completed. We show that the
quantity , where is the average dynamic shortest distance
and the success rate of completion of a search, is a consistent measure
for the quality of a search strategy. Taking the example of realistic searches
on scale-free networks, we find that scales with the system size as
, where decreases as the searching strategy is improved.
This measure is also shown to be sensitive to the distintinguishing
characteristics of networks. In this new approach, a dynamic small world (DSW)
effect is said to exist when . We show that such a DSW indeed
exists in social networks in which the linking probability is dependent on
social distances.Comment: Text revised, references added; accepted version in Journal of
Statistical Mechanic
Scale-free networks with tunable degree distribution exponents
We propose and study a model of scale-free growing networks that gives a
degree distribution dominated by a power-law behavior with a model-dependent,
hence tunable, exponent. The model represents a hybrid of the growing networks
based on popularity-driven and fitness-driven preferential attachments. As the
network grows, a newly added node establishes new links to existing nodes
with a probability based on popularity of the existing nodes and a
probability based on fitness of the existing nodes. An explicit form of
the degree distribution is derived within a mean field approach. For
reasonably large , , where the
function is dominated by the behavior of for small
values of and becomes -independent as , and is a
model-dependent exponent. The degree distribution and the exponent
are found to be in good agreement with results obtained by extensive numerical
simulations.Comment: 12 pages, 2 figures, submitted to PR
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
A network-based threshold model for the spreading of fads in society and markets
We investigate the behavior of a threshold model for the spreading of fads
and similar phenomena in society. The model is giving the fad dynamics and is
intended to be confined to an underlying network structure. We investigate the
whole parameter space of the fad dynamics on three types of network models. The
dynamics we discover is rich and highly dependent on the underlying network
structure. For some range of the parameter space, for all types of substrate
networks, there are a great variety of sizes and life-lengths of the fads --
what one see in real-world social and economical systems
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