Dynamic hierarchies in temporal directed networks

Graph representation learning (also known as network embedding) has been extensively researched with varying levels of granularity, ranging from nodes to graphs. While most prior work in this area focuses on node-level representation, limited research has been conducted on graph-level embedding, particularly for dynamic or temporal networks. However, learning low-dimensional graph-level representations for dynamic networks is critical for various downstream graph retrieval ta...

Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on temporal networks -- networks where we have explicit information about the time of the interaction, not only who interacts with whom. We contrast a type of greedy navigation -- where agents follow paths that would have worked well in the past -...

Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, it is today possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by a...

This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major reason for the popularity of the field of dynamic networks is its applicability in a number of diverse fields. The field of dynamic networks is in its infancy and there are so many avenues that need to be explored. From developing network g...

Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it's urgent and significant to focus on structural controllability of temporal networks, which nowadays is still an untouched topic. We develop graphic tools to study the structural controllability of temporal networks, identifying the intrinsic mechanism of the ability of indiv...

There is an ever-increasing interest in investigating dynamics in time-varying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. I...

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks present dynamic behavior, including topological evolution, feature evolution, and diffusion. Therefore, several methods for embedding dynamic graphs have been proposed to learn network representations over time, facing novel challenges, such as...

Betweenness centrality has been extensively studied since its introduction in 1977 as a measure of node importance in graphs. This measure has found use in various applications and has been extended to temporal graphs with time-labeled edges. Recent research by Bu{\ss} et al. \cite{buss2020algorithmic} and Rymar et al. \cite{rymar2021towards} has shown that it is possible to compute the shortest path betweenness centrality of all nodes in a temporal graph in $O(n^3\,T^2)$ and...

Social hierarchy (i.e., pyramid structure of societies) is a fundamental concept in sociology and social network analysis. The importance of social hierarchy in a social network is that the topological structure of the social hierarchy is essential in both shaping the nature of social interactions between individuals and unfolding the structure of the social networks. The social hierarchy found in a social network can be utilized to improve the accuracy of link prediction, pr...

Timestamped relational datasets consisting of records between pairs of entities are ubiquitous in data and network science. For applications like peer-to-peer communication, email, social network interactions, and computer network security, it makes sense to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies the complex...