Related papers: Testability of minimum balanced multiway cut densi…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
The set of relevant cuts in a graph is the union of all minimum weight bases of the cut space. A cut is relevant if and only if it is the a minimum weight cut between two distinct vertices. Moreover, we give a characterization in terms of…
We study large-scale systems operating under the JSQ$(d)$ policy in the presence of stringent task-server compatibility constraints. Consider a system with $N$ identical single-server queues and $M(N)$ task types, where each server is able…
A way to associate unweighted graphs from weighted ones is presented, such that linear stable equilibria of the Kuramoto homogeneous model associated to both graphs coincide, i.e., equilibria of the system $\dot\theta_i = \sum_{j \sim i}…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
For a fixed number of colors, we show that, in node-weighted split graphs, cographs, and graphs of bounded tree-width, one can determine in polynomial time whether a proper list-coloring of the vertices of a graph such that the total weight…
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under…
We study the following version of cut sparsification. Given a large edge-weighted network $G$ with $k$ terminal vertices, compress it into a smaller network $H$ with the same terminals, such that every minimum terminal cut in $H$…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete…
We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
We propose $\beta$-graph embedding for robustly learning feature vectors from data vectors and noisy link weights. A newly introduced empirical moment $\beta$-score reduces the influence of contamination and robustly measures the difference…