Predicting Graph Categories from Structural Properties

Complex networks are often categorized according to the underlying phenomena that they represent such as molecular interactions, re-tweets, and brain activity. In this work, we investigate the problem of predicting the category (domain) of arbitrary networks. This includes complex networks from different domains as well as synthetically generated graphs from five different network models. A classification accuracy of 96.6% is achieved using a random forest classifier with both real and synthetic networks. This work makes two important findings. First, our results indicate that complex networks from various domains have distinct structural properties that allow us to predict with high accuracy the category of a new previously unseen network. Second, synthetic graphs are trivial to classify as the classification model can predict with near-certainty the network model used to generate it. Overall, the results demonstrate that networks drawn from different domains (and network models) are trivial to distinguish using only a handful of simple structural properties

Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of pre-defined topologies is via degree-preserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties and tunable realistic assortativity. In our approach, two distinct populations of nodes are added to an initial network seed: one (the followers) that abides by usual preferential rules, and one (the potential leaders) connecting via anti-preferential attachments, i.e. selecting lower degree nodes for their initial links. The latter nodes come to develop a higher average degree, and convert eventually into the final hubs. Examining the evolution of links in Facebook, we present empirical validation for the connection between the initial anti-preferential attachment and long term high degree. Thus, our work sheds new light on the structure and evolution of social networks

Sampling motif-constrained ensembles of networks

The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency, or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this paper we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, net- works with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60% of the variation of motif profiles.Comment: Updated version, as published in the journal. 7 pages, 5 figures, one Supplemental Materia