298 research outputs found
Percolation on random networks with arbitrary k-core structure
The k-core decomposition of a network has thus far mainly served as a
powerful tool for the empirical study of complex networks. We now propose its
explicit integration in a theoretical model. We introduce a Hard-core Random
Network model that generates maximally random networks with arbitrary degree
distribution and arbitrary k-core structure. We then solve exactly the bond
percolation problem on the HRN model and produce fast and precise analytical
estimates for the corresponding real networks. Extensive comparison with
selected databases reveals that our approach performs better than existing
models, while requiring less input information.Comment: 9 pages, 5 figure
Growing networks of overlapping communities with internal structure
We introduce an intuitive model that describes both the emergence of
community structure and the evolution of the internal structure of communities
in growing social networks. The model comprises two complementary mechanisms:
One mechanism accounts for the evolution of the internal link structure of a
single community, and the second mechanism coordinates the growth of multiple
overlapping communities. The first mechanism is based on the assumption that
each node establishes links with its neighbors and introduces new nodes to the
community at different rates. We demonstrate that this simple mechanism gives
rise to an effective maximal degree within communities. This observation is
related to the anthropological theory known as Dunbar's number, i.e., the
empirical observation of a maximal number of ties which an average individual
can sustain within its social groups. The second mechanism is based on a
recently proposed generalization of preferential attachment to community
structure, appropriately called structural preferential attachment (SPA). The
combination of these two mechanisms into a single model (SPA+) allows us to
reproduce a number of the global statistics of real networks: The distribution
of community sizes, of node memberships and of degrees. The SPA+ model also
predicts (a) three qualitative regimes for the degree distribution within
overlapping communities and (b) strong correlations between the number of
communities to which a node belongs and its number of connections within each
community. We present empirical evidence that support our findings in real
complex networks.Comment: 14 pages, 8 figures, 2 table
Percolation and the effective structure of complex networks
Analytical approaches to model the structure of complex networks can be
distinguished into two groups according to whether they consider an intensive
(e.g., fixed degree sequence and random otherwise) or an extensive (e.g.,
adjacency matrix) description of the network structure. While extensive
approaches---such as the state-of-the-art Message Passing Approach---typically
yield more accurate predictions, intensive approaches provide crucial insights
on the role played by any given structural property in the outcome of dynamical
processes. Here we introduce an intensive description that yields almost
identical predictions to the ones obtained with MPA for bond percolation. Our
approach distinguishes nodes according to two simple statistics: their degree
and their position in the core-periphery organization of the network. Our
near-exact predictions highlight how accurately capturing the long-range
correlations in network structures allows to easily and effectively compress
real complex network data.Comment: 11 pages, 4 figure
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