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Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further exploring the networks themselves. Uncertainty, modelling procedures and measurement difficulties raise often insurmountable challenges in fully characterizing most of the known real-world networks; hence, the necessity to predict their unknown elements from the limited data currently available in order to estimate possible future relations and/or to unveil unmeasurable relations. In this work, we propose a deep learning approach to this problem based on Graph Convolutional Networks for predicting networks while preserving their original structural properties. The study reveals that this method can preserve scale-free and small-world properties of complex networks when predicting their unknown parts, a feature lacked by the up-to-date conventional methods. An external validation realized by testing the approach on biological networks confirms the results, initially obtained on artificial data. Moreover, this process provides new insights into the retainability of network structure properties in network prediction. We anticipate that our work could inspire similar approaches in other research fields as well, where unknown mechanisms behind complex systems need to be revealed by combining machine-based and experiment-based methods.
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Predicting the future evolution of complex systems is one of the main challenges in complexity science. Based on a current snapshot of a network, link prediction algorithms aim to predict its future evolution. We apply here link prediction algorithms to data on the international trade between countries. This data can be represented as a complex network where links connect countries with the products that they export. Link prediction techniques based on heat and mass diffusion processes are employed to obtain predictions for products exported in the future. These baseline predictions are improved using a recent metric of country fitness and product similarity. The overall best results are achieved with a newly developed metric of product similarity which takes advantage of causality in the network evolution.
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions than the ones obtained by the direct application of the algorithm. However, the procedure requires the calculation of the consensus matrix, which can be quite dense if (some of) the clusters of the input partitions are large. Consequently, the complexity can get dangerously close to quadratic, which makes the technique inapplicable on large graphs. Here we present a fast variant of consensus clustering, which calculates the consensus matrix only on the links of the original graph and on a comparable number of additional node pairs, suitably chosen. This brings the complexity down to linear, while the performance remains comparable as the full technique. Therefore, our fast consensus clustering procedure can be applied on networks with millions of nodes and links.
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resilience with an error of 5%.
We present a new layout algorithm for complex networks that combines a multi-scale approach for community detection with a standard force-directed design. Since community detection is computationally cheap, we can exploit the multi-scale approach to generate network configurations with close-to-minimal energy very fast. As a further asset, we can use the knowledge of the community structure to facilitate the interpretation of large networks, for example the network defined by protein-protein interactions.
Interactions between humans give rise to complex social networks that are characterized by heterogeneous degree distribution, weight-topology relation, overlapping community structure, and dynamics of links. Understanding such networks is a primary goal of science due to serving as the scaffold for many emergent social phenomena from disease spreading to political movements. An appropriate tool for studying them is agent-based modeling, in which nodes, representing persons, make decisions about creating and deleting links, thus yielding various macroscopic behavioral patterns. Here we focus on studying a generalization of the weighted social network model, being one of the most fundamental agent-based models for describing the formation of social ties and social networks. This Generalized Weighted Social Network (GWSN) model incorporates triadic closure, homophilic interactions, and various link termination mechanisms, which have been studied separately in the previous works. Accordingly, the GWSN model has an increased number of input parameters and the model behavior gets excessively complex, making it challenging to clarify the model behavior. We have executed massive simulations with a supercomputer and using the results as the training data for deep neural networks to conduct regression analysis for predicting the properties of the generated networks from the input parameters. The obtained regression model was also used for global sensitivity analysis to identify which parameters are influential or insignificant. We believe that this methodology is applicable for a large class of complex network models, thus opening the way for more realistic quantitative agent-based modeling.
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