Related papers: Beyond the locally tree-like approximation for per…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…
Graph neural networks compute node representations by performing multiple message-passing steps that consist in local aggregations of node features. Having deep models that can leverage longer-range interactions between nodes is hindered by…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics.…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
Tree-based protocols are ubiquitous in distributed systems. They are flexible, they perform generally well, and, in static conditions, their analysis is mostly simple. Under churn, however, node joins and failures can have complex global…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation…
In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirical effect of one-way streets in about $140$ cities in the…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
We propose a novel method for approximate inference in Bayesian networks (BNs). The idea is to sample data from a BN, learn a latent tree model (LTM) from the data offline, and when online, make inference with the LTM instead of the…
We propose a new method for hierarchical clustering based on the optimisation of a cost function over trees of limited depth, and we derive a message--passing method that allows to solve it efficiently. The method and algorithm can be…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…