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

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, the authors focus on the inference methods rooted in statistical physics and information theory. The discussion is organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections

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

Reconstructing networks

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, we shall focus on the inference methods rooted in statistical physics and information theory. The discussion will be organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections.Comment: 107 pages, 25 figure