2 research outputs found
Factorization threshold models for scale-free networks generation
Many real networks such as the World Wide Web, financial, biological,
citation and social networks have a power-law degree distribution. Networks
with this feature are also called scale-free. Several models for producing
scale-free networks have been obtained by now and most of them are based on the
preferential attachment approach. We will offer the model with another
scale-free property explanation. The main idea is to approximate the network's
adjacency matrix by multiplication of the matrices and , where is
the matrix of vertices' latent features. This approach is called matrix
factorization and is successfully used in the link prediction problem. To
create a generative model of scale-free networks we will sample latent features
from some probabilistic distribution and try to generate a network's
adjacency matrix. Entries in the generated matrix are dot products of latent
features which are real numbers. In order to create an adjacency matrix, we
approximate entries with the Boolean domain . We have incorporated
the threshold parameter into the model for discretization of a dot
product. Actually, we have been influenced by the geographical threshold models
which were recently proven to have good results in a scale-free networks
generation. The overview of our results is the following. First, we will
describe our model formally. Second, we will tune the threshold in
order to generate sparse growing networks. Finally, we will show that our model
produces scale-free networks with the fixed power-law exponent which equals
two. In order to generate oriented networks with tunable power-law exponents
and to obtain other model properties, we will offer different modifications of
our model. Some of our results will be demonstrated using computer simulation