Related papers: Optimal k-centers of a graph: a control-theoretic …
In this work, we present a new algorithm to approximate the percolation centrality of every node in a graph. Such a centrality measure quantifies the importance of the vertices in a network during a contagious process. In this paper, we…
Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the…
The metric dimension of a graph is the minimum number of landmark vertices required so that every vertex can be uniquely identified by its distances to the landmarks. This parameter captures the fundamental tradeoff between compact…
Let $G$ be a connected graph. The eccentricity of a path $P$, denoted by ecc$_G(P)$, is the maximum distance from $P$ to any vertex in $G$. In the \textsc{Central path} (CP) problem our aim is to find a path of minimum eccentricity. This…
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…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
We explore a connection between geodesic nets and quantum graphs optimising certain functionals from spectral theory. For surfaces, critical metrics for the normalised $k^{\mathrm{th}}$ eigenvalue of the Laplacian give rise to isometric…
We determine the size of $k$-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, $n$-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a kernel $W:[0,1]^2\to [0,+\infty)$ in…
In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…
Most network studies rely on an observed network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics,…
For an integer $k\geq 1$, the objective of \textsc{$k$-Geodesic Center} is to find a set $\mathcal{C}$ of $k$ isometric paths such that the maximum distance between any vertex $v$ and $\mathcal{C}$ is minimised. Introduced by Gromov,…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
The mobile robot dispersion problem on graphs asks $k\leq n$ robots placed initially arbitrarily on the nodes of an $n$-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of…
Decentralized optimization is effective to save communication in large-scale machine learning. Although numerous algorithms have been proposed with theoretical guarantees and empirical successes, the performance limits in decentralized…
We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
Centrality metrics play a crucial role in network analysis, while the choice of specific measures significantly influences the accuracy of conclusions as each measure represents a unique concept of node importance. Among over 400 proposed…