We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the node-normalized cut (also called cut ratio) and the edge-normalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria. The energy model that corresponds to the edge-normalized cut differs from the other ...

17 graph. The cuts of G are the minimal dependent sets of a matroid T ? (G) on the edge set E. A matroid T is cographic if there exists some graph G such that T is isomorphic to the cut matroid T ? (G). Every cographic matroid is representable over any eld 18]. Therefore if an access structure A has a cographic appropriate matroid, then A is universally ideal. Unlike graphic matroids, we do not...

The problem of finding duplicates in data is ubiquitous in data mining. We cast the problem of finding duplicates in sequential data into a poly-cut problem on a fully connected graph. The edge weights can be identified with parameterized pairwise similarities between objects that are optimized by structural support vector machines on labeled training sets. Our approach adapts the similarity me...

We propose and test a new linearisation technique for the Binary Quadratic Problems (BQPs). We computationally prove that the new formulation, called Extended Linear Formulation, can be effective for different classes of problems in practice. Our tests are based on two sets of classical BQPs from the literature, i.e., the Unconstrained BQP and the Maximum Cut of edge-weighted graphs. Finally we...

A cut edge in a graph G is an edge whose removal increases the number of connected components of G. In this paper we determine the maximum number of cut edges in a connected d-regular graph G of order p.

It is already known that for very small edge cuts in graphs, the crossing number of the graph is at least the sum of the crossing number of (slightly augmented) components resulting from the cut. Under stronger connectivity condition in each cut component that was formalized as a graph operation called zip product, a similar result was obtained for edge cuts of any size, and a natural question ...

We analyze a radius bone fragment of a raven (Corvus corax) from Zaskalnaya VI rock shelter, Crimea. The object bears seven notches and comes from an archaeological level attributed to a Micoquian industry dated to between 38 and 43 cal kyr BP. Our study aims to examine the degree of regularity and intentionality of this set of notches through their technological and morphometric analysis, comp...

A classical result in undirected edge-capaciated networks is the approximate optimality of routing (flow) for multiple-unicast: the min-cut upper bound is within a logarithmic factor of the number of sources of the max flow [2, 3]. In this paper we focus on extending this result to a more general network model, where there are joint polymatroidal constraints on the rates of the edges that meet ...