2 research outputs found
Coexistence of opposite opinions in a network with communities
The Majority Rule is applied to a topology that consists of two coupled
random networks, thereby mimicking the modular structure observed in social
networks. We calculate analytically the asymptotic behaviour of the model and
derive a phase diagram that depends on the frequency of random opinion flips
and on the inter-connectivity between the two communities. It is shown that
three regimes may take place: a disordered regime, where no collective
phenomena takes place; a symmetric regime, where the nodes in both communities
reach the same average opinion; an asymmetric regime, where the nodes in each
community reach an opposite average opinion. The transition from the asymmetric
regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure
Modeling and verifying a broad array of network properties
Motivated by widely observed examples in nature, society and software, where
groups of already related nodes arrive together and attach to an existing
network, we consider network growth via sequential attachment of linked node
groups, or graphlets. We analyze the simplest case, attachment of the three
node V-graphlet, where, with probability alpha, we attach a peripheral node of
the graphlet, and with probability (1-alpha), we attach the central node. Our
analytical results and simulations show that tuning alpha produces a wide range
in degree distribution and degree assortativity, achieving assortativity values
that capture a diverse set of many real-world systems. We introduce a
fifteen-dimensional attribute vector derived from seven well-known network
properties, which enables comprehensive comparison between any two networks.
Principal Component Analysis (PCA) of this attribute vector space shows a
significantly larger coverage potential of real-world network properties by a
simple extension of the above model when compared against a classic model of
network growth.Comment: To appear in Europhysics Letter