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We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
Betweeness centrality is one of the most important concepts in graph analysis. It was recently extended to link streams, a graph generalization where links arrive over time. However, its computation raises non-trivial issues, due in…
We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation…
We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…
We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.
Temporal social networks of human interactions are preponderant in understanding the fundamental patterns of human behavior. In these networks, interactions occur locally between individuals (i.e., nodes) who connect with each other at…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
Advances in public transit modeling and smart card technologies can reveal detailed contact patterns of passengers. A natural way to represent such contact patterns is in the form of networks. In this paper we utilize known contact patterns…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
Human navigation has been a topic of interest in spatial cognition from the past few decades. It has been experimentally observed that humans accomplish the task of way-finding a destination in an unknown environment by recognizing…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
Street networks, as one of the oldest infrastructures of transport in the world, play a significant role in modernization, sustainable development, and human daily activities in both ancient and modern times. Although street networks have…