Related papers: L1 Prominence Measures for Directed Graphs
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of…
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…
In this paper, we define several measures induced by a finite directed graph. The study themselves is interesting ont only in the noncommutative probability point of view but also in the algebraic structure point of view, since to define…
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…
Dismantling criminal networks or containing epidemics or misinformation through node removal is a well-studied problem. To evaluate the effectiveness of such efforts, one must measure the strength of the network before and after node…
The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is…
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
Causal structure discovery from observations can be improved by integrating background knowledge provided by an expert to reduce the hypothesis space. Recently, Large Language Models (LLMs) have begun to be considered as sources of prior…
We explore depth measures for flow hierarchy in directed networks. We define two measures -- rooted depth and relative depth, and discuss differences between them. We investigate how the two measures behave in random Erdos-Renyi graphs of…
We study the lobby index (l-index for short) as a local node centrality measure for complex networks. The l-inde is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of…
Long-range dependencies are critical for effective graph representation learning, yet most existing datasets focus on small graphs tailored to inductive tasks, offering limited insight into long-range interactions. Current evaluations…
Network centrality measures play a crucial role in understanding graph structures, assessing the importance of nodes, paths, or cycles based on directed or reciprocal interactions encoded by vertices and edges. Estrada and Ross extended…
Existing graph layout algorithms are usually not able to optimize all the aesthetic properties desired in a graph layout. To evaluate how well the desired visual features are reflected in a graph layout, many readability metrics have been…
Centrality represents a fundamental research field in complex network analysis, where centrality measures identify important vertices within networks. Over the years, researchers have developed diverse centrality measures from varied…
This work proposes a framework LGKDE that learns kernel density estimation for graphs. The key challenge in graph density estimation lies in effectively capturing both structural patterns and semantic variations while maintaining…
In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized…
Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…
We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The…