Efficiently Counting Complex Multilayer Temporal Motifs in Large-Scale Networks

This paper proposes novel algorithms for efficiently counting complex network motifs in dynamic networks that are changing over time. Network motifs are small characteristic configurations of a few nodes and edges, and have repeatedly been shown to provide insightful information for understanding the meso-level structure of a network. Here, we deal with counting more complex temporal motifs in large-scale networks that may consist of millions of nodes and edges. The first contribution is an efficient approach to count temporal motifs in multilayer networks and networks with partial timing, two prevalent aspects of many real-world complex networks. We analyze the complexity of these algorithms and empirically validate their performance on a number of real-world user communication networks extracted from online knowledge exchange platforms. Among other things, we find that the multilayer aspects provide significant insights in how complex user interaction patterns differ substantially between online platforms. The second contribution is an analysis of the viability of motif counting algorithms for motifs that are larger than the triad motifs studied in previous work. We provide a novel categorization of motifs of size four, and determine how and at what computational cost these motifs can still be counted efficiently. In doing so, we delineate the “computational frontier” of temporal motif counting algorithms.Algorithms and the Foundations of Software technolog

Principal Patterns on Graphs: Discovering Coherent Structures in Datasets

Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and scalable framework for retrieving and analyzing recurring patterns of activity on graphs. Our method relies on a novel type of multilayer graph that encodes the spreading or propagation of events between successive time steps. We demonstrate the versatility of our method by applying it on three different real-world examples. Firstly, we study how rumor spreads on a social network. Secondly, we reveal congestion patterns of pedestrians in a train station. Finally, we show how patterns of audio playlists can be used in a recommender system. In each example, relevant information previously hidden in the data is extracted in a very efficient manner, emphasizing the scalability of our method. With a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server

A Network Science perspective of Graph Convolutional Networks: A survey

The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the perspective of network structure, such as the centrality measures, the clustering coefficient, and motifs and graphlets, and they have become basic tools for studying and understanding graphs. In comparison, graph neural networks, especially graph convolutional networks (GCNs), are particularly effective at integrating node features into graph structures via neighbourhood aggregation and message passing, and have been shown to significantly improve the performances in a variety of learning tasks. These two classes of methods are, however, typically treated separately with limited references to each other. In this work, aiming to establish relationships between them, we provide a network science perspective of GCNs. Our novel taxonomy classifies GCNs from three structural information angles, i.e., the layer-wise message aggregation scope, the message content, and the overall learning scope. Moreover, as a prerequisite for reviewing GCNs via a network science perspective, we also summarise traditional structural measures and propose a new taxonomy for them. Finally and most importantly, we draw connections between traditional structural approaches and graph convolutional networks, and discuss potential directions for future research

Investigating scientific mobility in co-authorship networks using multilayer temporal motifs

Algorithms and the Foundations of Software technolog

Privacy and Anonymization of Neighborhoods in Multiplex Networks

Since the beginning of the digital age, the amount of available data on human behaviour has dramatically increased, along with the risk for the privacy of the represented subjects. Since the analysis of those data can bring advances to science, it is important to share them while preserving the subjects' anonymity. A significant portion of the available information can be modelled as networks, introducing an additional privacy risk related to the structure of the data themselves. For instance, in a social network, people can be uniquely identifiable because of the structure of their neighborhood, formed by the amount of their friends and the connections between them. The neighborhood's structure is the target of an identity disclosure attack on released social network data, called neighborhood attack. To mitigate this threat, algorithms to anonymize networks have been proposed. However, this problem has not been deeply studied on multiplex networks, which combine different social network data into a single representation. The multiplex network representation makes the neighborhood attack setting more complicated, and adds information that an attacker can use to re-identify subjects. This thesis aims to understand how multiplex networks behave in terms of anonymization difficulty and neighborhood attack. We present two definitions of multiplex neighborhoods, and discuss how the fraction of nodes with unique neighborhoods can be affected. Through analysis of network models, we study the variation of the uniqueness of neighborhoods in networks with different structure and characteristics. We show that the uniqueness of neighborhoods has a linear trend depending on the network size and average degree. If the network has a more random structure, the uniqueness decreases significantly when the network size increases. On the other hand, if the local structure is more pronounced, the uniqueness is not strongly influenced by the number of nodes. We also conduct a motif analysis to study the recurring patterns that can make social networks' neighborhoods less unique. Lastly, we propose an algorithm to anonymize a pair of multiplex neighborhoods. This algorithm is the core building block that can be used in a method to prevent neighborhood attacks on multiplex networks