Related papers: Preorder Construct on Simple Undirected Graphs
We give a self-contained introduction to the theory of directed graphs, leading up to the relationship between the Perron-Frobenius eigenvectors of a graph and its autocatalytic sets. Then we discuss a particular dynamical system on a fixed…
Formation mechanisms are fundamental to the study of complex networks, but learning them from observations is challenging. In real-world domains, one often has access only to the final constructed graph, instead of the full construction…
Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
Graph classification has practical applications in diverse fields. Recent studies show that graph-based machine learning models are especially vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. By adding or…
The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an…
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Network visualisation techniques are important tools for the exploratory analysis of complex systems. While these methods are regularly applied to visualise data on complex networks, we increasingly have access to time series data that can…
We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
Inferring the underlying graph topology that characterizes structured data is pivotal to many graph-based models when pre-defined graphs are not available. This paper focuses on learning graphs in the case of sequential data in dynamic…
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…
An algorithm for generating the structure of a directed acyclic graph from data using the notion of causal input lists is presented. The algorithm manipulates the ordering of the variables with operations which very much resemble arc…