Related papers: Cycle Analysis of Directed Acyclic Graphs

This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…

We propose a method to identify nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. We show that it is necessary and sufficient to measure all the sinks to identify any…

The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…

We analyze the identifiability of directed acyclic graphs in the case of partial excitation and measurement. We consider an additive model where the nonlinear functions located in the edges depend only on a past input, and we analyze the…

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…

Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…

The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the…

Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…

We study the growth of networks from a set of isolated ground nodes by the addition of one new node per time step and also of a fixed number of directed edges leading from the new node to randomly selected nodes already in the network. A…

Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…

We develop a novel convolutional architecture tailored for learning from data defined over directed acyclic graphs (DAGs). DAGs can be used to model causal relationships among variables, but their nilpotent adjacency matrices pose unique…

We address the question how a given connection structure (directed graph) can be realised as a heteroclinic network that is complete in the sense that it contains all unstable manifolds of its equilibria. For a directed graph consisting of…

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…

We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is…

Directed networks such as gene regulation networks and neural networks are connected by arcs (directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which lead to complex…

We introduce a framework for network analysis based on random walks on directed acyclic graphs where the probability of passing through a given node is the key ingredient. We illustrate its use in evaluating the mutual influence of nodes…

We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…