Related papers: A Theory for Backtrack-Downweighted Walks
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in…
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…
We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm of the…
Quantization based model compression serves as high performing and fast approach for inference that yields models which are highly compressed when compared to their full-precision floating point counterparts. The most extreme quantization…
We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled…
Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…
Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…
We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of…
Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…
In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…
Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of sets of steps from a predefined set such that all possible…
Empirical research on world cities often draws on Taylor's (2001) notion of an 'interlocking network model', in which office networks of globalized service firms are assumed to shape the spatialities of urban networks. In spite of its many…
We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with…
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence.…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…
Feller's book An Introduction to Probability Theory and Its Application discusses statistics corresponding to sequences of coin tosses, with a dollar being won or lost depending on the outcome of each toss. This is equivalent to analyzing…
By considering the eigenratio of the Laplacian of the connection graph as synchronizability measure, we propose a procedure for weighting dynamical networks to enhance theirsynchronizability. The method is based on node and edge betweenness…
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…