Machine learning dismantling and early-warning signals of disintegration in complex systems

Geometric Deep Learning sub-network extraction for Maximum Clique Enumeration

The paper presents an algorithm to approach the problem of Maximum Clique Enumeration, a well known NP-hard problem that have several real world applications. The proposed solution, called LGP-MCE, exploits Geometric Deep Learning, a Machine Learning technique on graphs, to filter out nodes that do not belong to maximum cliques and then applies an exact algorithm to the pruned network. To assess the LGP-MCE, we conducted multiple experiments using a substantial dataset of real-world networks, varying in size, density, and other characteristics. We show that LGP-MCE is able to drastically reduce the running time, while retaining all the maximum cliques.

Exploring the landscape of dismantling strategies based on the community structure of networks

Network dismantling is a relevant research area in network science, gathering attention both from a theoretical and an operational point of view. Here, we propose a general framework for dismantling that prioritizes the removal of nodes that bridge together different network communities. The strategies we detect are not unique, as they depend on the specific realization of the community detection algorithm considered. However, when applying the methodology to some synthetic benchmark and real-world networks we find that the dismantling performances are strongly robust, and do not depend on the specific algorithm. Thus, the stochasticity inherently present in many community detection algorithms allows to identify several strategies that have comparable effectiveness but require the removal of distinct subsets of nodes. This feature is highly relevant in operational contexts in which the removal of nodes is costly and allows to identify the least expensive strategy that still holds high effectiveness.

A Learning Convolutional Neural Network Approach for Network Robustness Prediction

Network robustness is critical for various societal and industrial networks against malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible for large-scale networks. In this article, an improved method for network robustness prediction is developed based on learning feature representation using the convolutional neural network (LFR-CNN). In this scheme, the higher-dimensional network data are compressed into lower-dimensional representations, which are then passed to a convolutional neural network to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that: 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly smaller prediction errors; 2) LFR-CNN is insensitive to the variation of the input network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; and 4) LFR-CNN not only accurately predicts the network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.

Inferring origin-destination distribution of agent transfer in a complex network using deep gated recurrent units

Predicting the origin-destination (OD) probability distribution of agent transfer is an important problem for managing complex systems. However, prediction accuracy of associated statistical estimators suffer from underdetermination. While specific techniques have been proposed to overcome this deficiency, there still lacks a general approach. Here, we propose a deep neural network framework with gated recurrent units (DNNGRU) to address this gap. Our DNNGRU is network-free, as it is trained by supervised learning with time-series data on the volume of agents passing through edges. We use it to investigate how network topologies affect OD prediction accuracy, where performance enhancement is observed to depend on the degree of overlap between paths taken by different ODs. By comparing against methods that give exact results, we demonstrate the near-optimal performance of our DNNGRU, which we found to consistently outperform existing methods and alternative neural network architectures, under diverse data generation scenarios.

GLD-Net: Deep Learning to Detect DDoS Attack via Topological and Traffic Feature Fusion

Distributed denial of service (DDoS) attacks are the most common means of cyberattacks against infrastructure, and detection is the first step in combating them. The current DDoS detection mainly uses the improvement or fusion of machine learning and deep learning methods to improve classification performance. However, most classifiers are trained with statistical flow features as input, ignoring topological connection changes. This one-sidedness affects the detection accuracy and cannot provide a basis for the distribution of attack sources for defense deployment. In this study, we propose a topological and flow feature-based deep learning method (GLD-Net), which simultaneously extracts flow and topological features from time-series flow data and exploits graph attention network (GAT) to mine correlations between non-Euclidean features to fuse flow and topological features. The long short-term memory (LSTM) network connected behind GAT obtains the node neighborhood relationship, and the fully connected layer is utilized to achieve feature dimension reduction and traffic type mapping. Experiments on the NSL-KDD2009 and CIC-IDS2017 datasets show that the detection accuracy of the GLD-Net method for two classifications (normal and DDoS flow) and three classifications (normal, fast DDoS flow, and slow DDoS flow) reaches 0.993 and 0.942, respectively. Compared with the existing DDoS attack detection methods, its average improvement is 0.11 and 0.081, respectively. In addition, the correlation coefficient between the detection accuracy of attack flow and the four source distribution indicators ranges from 0.7 to 0.83, which lays a foundation for the inference of attack source distribution. Notably, we are the first to fuse topology and flow features and achieve high-performance DDoS attack intrusion detection through graph-style neural networks. This study has important implications for related research and development of network security systems in other fields.

Neural extraction of multiscale essential structure for network dismantling

Diverse real world systems can be abstracted as complex networks consisting of nodes and edges as functional components. Percolation theory has shown that the failure of a few of nodes could lead to the collapse of a whole network, which brings up the network dismantling problem: How to select the least number of nodes to decompose a network into disconnected components each smaller than a predefined threshold? For its NP-hardness, many heuristic approaches have been proposed to measure and rank each node according to its importance to network structural stability. However, these measures are from a uniscale viewpoint by regarding one complex network as a flatted topology. In this article, we argue that nodes' structural importance can be measured in different scales of network topologies. Built upon recent deep learning techniques, we propose a self-supervised learning based network dismantling framework (NEES), which can hierarchically merge some compact substructures to convert a network into a coarser one with fewer nodes and edges. During the merging process, we design neural models to extract essential structures and utilize self-attention mechanisms to learn nodes' importance hierarchy in each scale. Experiments on real world networks and synthetic model networks show that the proposed NEES outperforms the state-of-the-art schemes in most cases in terms of removing the least number of target nodes to dismantle a network. The dismantling effectiveness of our neural extraction framework also highlights the emerging role of multi-scale essential structures.

From the origin of life to pandemics: emergent phenomena in complex systems

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This non-trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems-from physical to biological and social-and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the theme issue Emergent phenomena in complex physical and socio-technical systems: from cells to societies, where we provide a synthesis of the contents tackled in the issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Link Prediction in Time Varying Social Networks

Predicting new links in complex networks can have a large societal impact. In fact, many complex systems can be modeled through networks, and the meaning of the links depend on the system itself. For instance, in social networks, where the nodes are users, links represent relationships (such as acquaintance, friendship, etc.), whereas in information spreading networks, nodes are users and content and links represent interactions, diffusion, etc. However, while many approaches involve machine learning-based algorithms, just the most recent ones account for the topology of the network, e.g., geometric deep learning techniques to learn on graphs, and most of them do not account for the temporal dynamics in the network but train on snapshots of the system at a given time. In this paper, we aim to explore Temporal Graph Networks (TGN), a Graph Representation Learning-based approach that natively supports dynamic graphs and assigns to each event (link) a timestamp. In particular, we investigate how the TGN behaves when trained under different temporal granularity or with various event aggregation techniques when learning the inductive and transductive link prediction problem on real social networks such as Twitter, Wikipedia, Yelp, and Reddit. We find that initial setup affects the temporal granularity of the data, but the impact depends on the specific social network. For instance, we note that the train batch size has a strong impact on Twitter, Wikipedia, and Yelp, while it does not matter on Reddit.