Abstract: A lattice network is a special type of network in
which all nodes have the same number of links, and its boundary
conditions are periodic. The most basic lattice network is the ring, a
one-dimensional network with periodic border conditions. In contrast,
the Cartesian product of d rings forms a d-dimensional lattice
network. An analytical expression currently exists for the clustering
coefficient in this type of network, but the theoretical value is valid
only up to certain connectivity value; in other words, the analytical
expression is incomplete. Here we obtain analytically the clustering
coefficient expression in d-dimensional lattice networks for any link
density. Our analytical results show that the clustering coefficient for
a lattice network with density of links that tend to 1, leads to the
value of the clustering coefficient of a fully connected network. We
developed a model on criminology in which the generalized clustering
coefficient expression is applied. The model states that delinquents
learn the know-how of crime business by sharing knowledge, directly
or indirectly, with their friends of the gang. This generalization shed
light on the network properties, which is important to develop new
models in different fields where network structure plays an important
role in the system dynamic, such as criminology, evolutionary game
theory, econophysics, among others.
Abstract: The world wide web network is a network with a
complex topology, the main properties of which are the distribution
of degrees in power law, A low clustering coefficient and a weak
average distance. Modeling the web as a graph allows locating the
information in little time and consequently offering a help in the
construction of the research engine. Here, we present a model based
on the already existing probabilistic graphs with all the aforesaid
characteristics. This work will consist in studying the web in order to
know its structuring thus it will enable us to modelize it more easily
and propose a possible algorithm for its exploration.
Abstract: Brain functional networks based on resting-state EEG
data were compared between patients with mild Alzheimer’s disease
(mAD) and matched patients with amnestic subtype of mild cognitive
impairment (aMCI). We integrated the time–frequency cross mutual
information (TFCMI) method to estimate the EEG functional
connectivity between cortical regions and the network analysis based
on graph theory to further investigate the alterations of functional
networks in mAD compared with aMCI group. We aimed at
investigating the changes of network integrity, local clustering,
information processing efficiency, and fault tolerance in mAD brain
networks for different frequency bands based on several topological
properties, including degree, strength, clustering coefficient, shortest
path length, and efficiency. Results showed that the disruptions of
network integrity and reductions of network efficiency in mAD
characterized by lower degree, decreased clustering coefficient, higher
shortest path length, and reduced global and local efficiencies in the
delta, theta, beta2, and gamma bands were evident. The significant
changes in network organization can be used in assisting
discrimination of mAD from aMCI in clinical.
Abstract: This paper describes a novel approach for deriving
modules from protein-protein interaction networks, which combines
functional information with topological properties of the network.
This approach is based on weighted clustering coefficient, which
uses weights representing the functional similarities between the
proteins. These weights are calculated according to the semantic
similarity between the proteins, which is based on their Gene
Ontology terms. We recently proposed an algorithm for identification
of functional modules, called SWEMODE (Semantic WEights for
MODule Elucidation), that identifies dense sub-graphs containing
functionally similar proteins. The rational underlying this approach is
that each module can be reduced to a set of triangles (protein triplets
connected to each other). Here, we propose considering semantic
similarity weights of all triangle-forming edges between proteins. We
also apply varying semantic similarity thresholds between
neighbours of each node that are not neighbours to each other (and
hereby do not form a triangle), to derive new potential triangles to
include in module-defining procedure. The results show an
improvement of pure topological approach, in terms of number of
predicted modules that match known complexes.