Random walks are ubiquitous in network science, for they are simple yet powerful models of diffusion and information exchange, they also allow to gather information about the network structure finding, e.g., communities, or the deepest node aka the [network median](https://gbertagnolli.github.io/publication/network-depth/). One of the main reasons of their success lies in their mathematics: they are Markov chains on a finite state space with transition probabilities prescribed by the network connectivity. Unfortunately, not all real dynamics satisfy the Markov property and so generalised random walks are needed. In this work, we extensively explore the self-avoiding random walk, and a variation thereof which embeds a resetting mechanism, as an efficient network exploration strategy inspired by the _run-and-tumble_ motion of some bacteria. A significant novelty in this work is provided by the statistical approach we used to describe the evolution of important network features during self-avoiding-type random walks, which are stochastic chains on an evolving state space with structure- and time-dependent transitions.
Many real systems (social groups, the brain, economic and transportation networks) display a particular organization of their hubs (nodes with a lot of connections): they are more densely connected among them than expected by chance. In other words, these rich nodes form clubs, called 'rich clubs'. How do these (structural) rich clubs reflect on dynamical processes taking place on the network? It depends on many aspects: of course, it depends on the dynamics, so here we focus on diffusion dynamics modelled through continuous-time random walks. Then, it also depends on which other types of structures are present in the network, and on their hierarchical relations. In brief: the presence of a strong structural does not imply the existence a strong functional rich club (easier diffusion among rich nodes). The vice versa is also true: functional rich clubs do not translate directly into denser connectivity among hubs. For more detail, and cool plots, see the paper!
Check out the R package diffudist, now also on CRAN! The diffudist package allows you to easily evaluate (and plot with ggplot2) diffusion distances between the nodes of a complex networks and, in so doing, analaysing the functional shape and diffusion geometry of your networks.
In 2017 Manlio De Domenico introduced the family of diffusion distances and induced geometry as a tool for the analysis of the functional organisation of complex networks. Its natural generalisation to multilayer networks was still missing and with this work we filled the gap providing (i) a rigorous mathematical definition of the diffusion distance(s) and induced space(s) in the framework of multilayer networks, (ii) the extension of the diffusion distance definition w.r.t. different random walk dynamics, and (iii) a detailed analysis of the interplay between layer topology, inter-layer connectivity, layer-layer correlations (in terms of edge/partition overlapping), and random walk dynamics.
We introduce in this study CovMulNet19, a comprehensive COVID-19 network containing all available known interactions involving SARS-CoV-2 proteins, interacting-human proteins, diseases and symptoms that are related to these human proteins, and compounds that can potentially target them.
Exchanging information is crucial for many real systems and consequently also assessing the how efficiently a system carries on this task. Here we assume that the pairwise communication efficiency is inversely proportional to their distance (metric on the network). Furthermore, we focus on the efficiency that can be quantified through the topology of and the flows on the network.
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as …
Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the underlying …
This is a small demo related to our (Giulia Bertagnolli, Claudio Agostinelli, Manlio De Domenico) recent work, Network depth: identifying median and contours in complex networks, Journal of Complex Networks 8 (4).