Related papers: An improved tree-graph bound

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes…

We establish an explicit lower bound for Kruskal's weak tree function at n=3, proving that tree(3) >= 844,424,930,131,960 = 3 * 2^48 - 8. This is achieved by constructing an explicit sequence of unlabeled rooted trees satisfying the…

Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…

Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these…

Urschel introduced a notion of nodal partitioning to prove an upper bound on the number of nodal decomposition of discrete Laplacian eigenvectors. The result is an analogue to the well-known Courant's nodal domain theorem on continuous…

There have been several recent attempts to improve the accuracy of grammar induction systems by bounding the recursive complexity of the induction model (Ponvert et al., 2011; Noji and Johnson, 2016; Shain et al., 2016; Jin et al., 2018).…

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index…

The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of…

The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…

We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing…

In this paper, we use tree partition schemes and an algebraic expression for the virial coefficients in terms of the cluster coefficients in order to derve upper bounds on the virial coefficients and consequently lower bounds on the radius…

We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small…

We prove that every $k$-list-critical graph ($k \ge 7$) on $n \ge k+2$ vertices has at least $\frac12 \left(k-1 + \frac{k-3}{(k-c)(k-1) + k-3}\right)n$ edges where $c = (k-3)\left(\frac12 - \frac{1}{(k-1)(k-2)}\right)$. This improves the…

Consider a uniform expanders family G_n with a uniform bound on the degrees. It is shown that for any p and c>0, a random subgraph of G_n obtained by retaining each edge, randomly and independently, with probability p, will have at most one…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions $d$ up to $d=5$. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method…

A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures…

We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of the Laplacian Spread Conjecture. We…