21 research outputs found
A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities
The hidden metric space behind complex network topologies is a fervid topic
in current network science and the hyperbolic space is one of the most studied,
because it seems associated to the structural organization of many real complex
systems. The Popularity-Similarity-Optimization (PSO) model simulates how
random geometric graphs grow in the hyperbolic space, reproducing strong
clustering and scale-free degree distribution, however it misses to reproduce
an important feature of real complex networks, which is the community
organization. The Geometrical-Preferential-Attachment (GPA) model was recently
developed to confer to the PSO also a community structure, which is obtained by
forcing different angular regions of the hyperbolic disk to have variable level
of attractiveness. However, the number and size of the communities cannot be
explicitly controlled in the GPA, which is a clear limitation for real
applications. Here, we introduce the nonuniform PSO (nPSO) model that,
differently from GPA, forces heterogeneous angular node attractiveness by
sampling the angular coordinates from a tailored nonuniform probability
distribution, for instance a mixture of Gaussians. The nPSO differs from GPA in
other three aspects: it allows to explicitly fix the number and size of
communities; it allows to tune their mixing property through the network
temperature; it is efficient to generate networks with high clustering. After
several tests we propose the nPSO as a valid and efficient model to generate
networks with communities in the hyperbolic space, which can be adopted as a
realistic benchmark for different tasks such as community detection and link
prediction
Latent Geometry Inspired Graph Dissimilarities Enhance Affinity Propagation Community Detection in Complex Networks
Affinity propagation is one of the most effective unsupervised pattern
recognition algorithms for data clustering in high-dimensional feature space.
However, the numerous attempts to test its performance for community detection
in complex networks have been attaining results very far from the state of the
art methods such as Infomap and Louvain. Yet, all these studies agreed that the
crucial problem is to convert the unweighted network topology in a
'smart-enough' node dissimilarity matrix that is able to properly address the
message passing procedure behind affinity propagation clustering. Here we
introduce a conceptual innovation and we discuss how to leverage network latent
geometry notions in order to design dissimilarity matrices for affinity
propagation community detection. Our results demonstrate that the latent
geometry inspired dissimilarity measures we design bring affinity propagation
to equal or outperform current state of the art methods for community
detection. These findings are solidly proven considering both synthetic
'realistic' networks (with known ground-truth communities) and real networks
(with community metadata), even when the data structure is corrupted by noise
artificially induced by missing or spurious connectivity
Intra-community link formation and modularity in ultracold growing hyperbolic networks
Hyperbolic network models, centered around the idea of placing nodes at
random in a hyperbolic space and drawing links according to a probability that
decreases as a function of the distance, provide a simple, yet also very
capable framework for grasping the small-world, scale-free, highly clustered
and modular nature of complex systems that are often referred to as real-world
networks. In the present work we study the community structure of networks
generated by the Popularity Similarity Optimization model (corresponding to one
of the fundamental, widely known hyperbolic models) when the temperature
parameter (responsible for tuning the clustering coefficient) is set to the
limiting value of zero. By focusing on the intra-community link formation we
derive analytical expressions for the expected modularity of a partitioning
consisting of equally sized angular sectors in the native disk representation
of the 2d hyperbolic space. Our formulas improve earlier results to a great
extent, being able to estimate the average modularity (measured by numerical
simulations) with high precision in a considerably larger range both in terms
of the model parameters and also the relative size of the communities with
respect to the entire network. These findings enhance our comprehension of how
modules form in hyperbolic networks. The existence of these modules is somewhat
unexpected, given the absence of explicit community formation steps in the
model definition