相关论文: Average Distance Queries through Weighted Samples …
We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O(n)$ distances to output a constant factor approximation to the average distance among those points, thus answering a…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
The biharmonic distance is a fundamental metric on graphs that measures the dissimilarity between two nodes, capturing both local and global structures. It has found applications across various fields, including network centrality, graph…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…
Let $G$ be a finite, simple connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The remoteness $\rho(G)$ of $G$ is the maximum of the average distances…
Closeness centrality, first considered by Bavelas (1948), is an importance measure of a node in a network which is based on the distances from the node to all other nodes. The classic definition, proposed by Bavelas (1950), Beauchamp…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…