Reconstructing propagation networks with temporal similarity

Backbone reconstruction in temporal networks from epidemic data

Many complex systems are characterized by time-varying patterns of interactions. These interactions comprise strong ties, driven by dyadic relationships, and weak ties, based on node-specific attributes. The interplay between strong and weak ties plays an important role on dynamical processes that could unfold on complex systems. However, seldom do we have access to precise information about the time-varying topology of interaction patterns. A particularly elusive question is to distinguish strong from weak ties, on the basis of the sole node dynamics. Building upon analytical results, we propose a statistically-principled algorithm to reconstruct the backbone of strong ties from data of a spreading process, consisting of the time series of individuals' states. Our method is numerically validated over a range of synthetic datasets, encapsulating salient features of real-world systems. Motivated by compelling evidence, we propose the integration of our algorithm in a targeted immunization strategy that prioritizes influential nodes in the inferred backbone. Through Monte Carlo simulations on synthetic networks and a real-world case study, we demonstrate the viability of our approach.

Data-based reconstruction of complex geospatial networks, nodal positioning and detection of hidden nodes

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.