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We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Matrix Factorization Techniques for Recommender Systems

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

Vital nodes identification in complex networks

Finding an optimal subset of nodes in a network that is able to efficiently disrupt the functioning of a corrupt or criminal organization or contain an epidemic or the spread of misinformation is a highly relevant problem of network science. In this paper, we address the generalized network-dismantling problem, which aims at finding a set of nodes whose removal from the network results in the fragmentation of the network into subcritical network components at minimal overall cost. Compared with previous formulations, we allow the costs of node removals to take arbitrary nonnegative real values, which may depend on topological properties such as node centrality or on nontopological features such as the price or protection level of a node. Interestingly, we show that nonunit costs imply a significantly different dismantling strategy. To solve this optimization problem, we propose a method which is based on the spectral properties of a node-weighted Laplacian operator and combine it with a fine-tuning mechanism related to the weighted vertex cover problem. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens more directions for understanding the vulnerability and robustness of complex systems.

https://www.pnas.org/content/pnas/116/14/6554.full.pdf

Generalized network dismantling.

Detection of patient zero can give new insights to epidemiologists about the nature of first transmissions into a population. In this Letter, we study the statistical inference problem of detecting the source of epidemics from a snapshot of spreading on an arbitrary network structure. By using exact analytic calculations and Monte Carlo estimators, we demonstrate the detectability limits for the susceptible infected-recovered model, which primarily depend on the spreading process characteristics. Finally, we demonstrate the applicability of the approach in a case of a simulated sexually transmitted infection spreading over an empirical temporal network of sexual interactions.

Identification of Patient Zero in Static and Temporal Networks: Robustness and Limitations

For recurrent neural networks trained on time series with target and exogenous variables, in addition to accurate prediction, it is also desired to provide interpretable insights into the data. In this paper, we explore the structure of LSTM recurrent neural networks to learn variable-wise hidden states, with the aim to capture different dynamics in multi-variable time series and distinguish the contribution of variables to the prediction. With these variable-wise hidden states, a mixture attention mechanism is proposed to model the generative process of the target. Then we develop associated training methods to jointly learn network parameters, variable and temporal importance w.r.t the prediction of the target variable. Extensive experiments on real datasets demonstrate enhanced prediction performance by capturing the dynamics of different variables. Meanwhile, we evaluate the interpretation results both qualitatively and quantitatively. It exhibits the prospect as an end-to-end framework for both forecasting and knowledge extraction over multi-variable data.

/pdf/exploring-interpretable-lstm-neural-networks-over-multi-9q9t1n7uwm.pdf

Exploring interpretable LSTM neural networks over multi-variable data

A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering

Motivated by recent financial crises, significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said regarding the influence of financial news on financial markets. We propose a novel measure of collective behaviour based on financial news on the Web, the News Cohesiveness Index (NCI), and we demonstrate that the index can be used as a financial market volatility indicator. We evaluate the NCI using financial documents from large Web news sources on a daily basis from October 2011 to July 2013 and analyse the interplay between financial markets and finance-related news. We hypothesise that strong cohesion in financial news reflects movements in the financial markets. Our results indicate that cohesiveness in financial news is highly correlated with and driven by volatility in financial markets.

/pdf/cohesiveness-in-financial-news-and-its-relation-to-market-5dmd2fslg2.pdf

Nino Antulov-Fantulin

Papers

Generalized network dismantling.

Identification of Patient Zero in Static and Temporal Networks: Robustness and Limitations

Exploring interpretable LSTM neural networks over multi-variable data

A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering

Cohesiveness in financial news and its relation to market volatility.