Related papers: Sharp Thresholds for Temporal Motifs and Doubling …
Temporal information is increasingly available as part of large network data sets. This information reveals sequences of link activations between network entities, which can expose underlying processes in the data. Examples include the…
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…
In 1964 Erd\H{o}s proved that $(1+\oh{1})) \frac{\eul \ln(2)}{4} k^2 2^{k}$ edges are sufficient to build a $k$-graph which is not two colorable. To this day, it is not known whether there exist such $k$-graphs with smaller number of edges.…
Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…
Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…
Temporal networks consist of timestamped directed interactions that may appear continuously in time, yet few studies have directly tackled the continuous-time modeling of networks. Here, we introduce a maximum-entropy approach to temporal…
We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is a uniform random hypergraph that contains a dense subhypergraph. We…
A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…
Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative…
Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…
Starting with the large deviation principle (LDP) for the Erd\H{o}s-R\'enyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph…
Among observables characterising the random exploration of a graph or lattice, the cover time, namely the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the…
A (directed) temporal graph is a (directed) graph whose edges are available only at specific times during its (discretized) lifetime $\tau$. In this setting, we ask that walks respect the temporal aspect by defining $\textit{temporal…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
In this paper, we study temporal graphs arising from mobility models, where vertices correspond to agents moving in space and edges appear each time two agents meet. We propose a rather natural one-dimensional model. If each pair of agents…
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…
Graph generative models are highly important for sharing surrogate data and benchmarking purposes. Real-world complex systems often exhibit dynamic nature, where the interactions among nodes change over time in the form of a temporal…
Over the last decade, there has been an increasing interest in temporal graphs, pushed by a growing availability of temporally-annotated network data coming from social, biological and financial networks. Despite the importance of analyzing…