24 research outputs found
Multiscale mixing patterns in networks
Assortative mixing in networks is the tendency for nodes with the same
attributes, or metadata, to link to each other. It is a property often found in
social networks manifesting as a higher tendency of links occurring between
people with the same age, race, or political belief. Quantifying the level of
assortativity or disassortativity (the preference of linking to nodes with
different attributes) can shed light on the factors involved in the formation
of links and contagion processes in complex networks. It is common practice to
measure the level of assortativity according to the assortativity coefficient,
or modularity in the case of discrete-valued metadata. This global value is the
average level of assortativity across the network and may not be a
representative statistic when mixing patterns are heterogeneous. For example, a
social network spanning the globe may exhibit local differences in mixing
patterns as a consequence of differences in cultural norms. Here, we introduce
an approach to localise this global measure so that we can describe the
assortativity, across multiple scales, at the node level. Consequently we are
able to capture and qualitatively evaluate the distribution of mixing patterns
in the network. We find that for many real-world networks the distribution of
assortativity is skewed, overdispersed and multimodal. Our method provides a
clearer lens through which we can more closely examine mixing patterns in
networks.Comment: 11 pages, 7 figure
Mean Field Analysis of Personalized PageRank with Implications for Local Graph Clustering
We analyse a mean-field model of Personalized PageRank (PPR) on the Erdős–Rényi (ER) random graph containing a denser planted ER subgraph. We investigate the regimes where the values of PPR concentrate around the mean-field value. We also study the optimization of the damping factor, the only parameter in PPR. Our theoretical results help to understand the applicability of PPR and its limitations for local graph clustering
Element-centric clustering comparison unifies overlaps and hierarchy
Clustering is one of the most universal approaches for understanding complex
data. A pivotal aspect of clustering analysis is quantitatively comparing
clusterings; clustering comparison is the basis for many tasks such as
clustering evaluation, consensus clustering, and tracking the temporal
evolution of clusters. In particular, the extrinsic evaluation of clustering
methods requires comparing the uncovered clusterings to planted clusterings or
known metadata. Yet, as we demonstrate, existing clustering comparison measures
have critical biases which undermine their usefulness, and no measure
accommodates both overlapping and hierarchical clusterings. Here we unify the
comparison of disjoint, overlapping, and hierarchically structured clusterings
by proposing a new element-centric framework: elements are compared based on
the relationships induced by the cluster structure, as opposed to the
traditional cluster-centric philosophy. We demonstrate that, in contrast to
standard clustering similarity measures, our framework does not suffer from
critical biases and naturally provides unique insights into how the clusterings
differ. We illustrate the strengths of our framework by revealing new insights
into the organization of clusters in two applications: the improved
classification of schizophrenia based on the overlapping and hierarchical
community structure of fMRI brain networks, and the disentanglement of various
social homophily factors in Facebook social networks. The universality of
clustering suggests far-reaching impact of our framework throughout all areas
of science