In [3,4,5], we treated edge weighted tetrahedra with a zero-sum condition on their triangles as the vertices of a graph Gi,n whose adjacency is given by the sharing of pairs ofedge-weighted triangles. In the present paper, we consider the situation modulo an odd positive integer n, so that we deal with hnite graph G'^,o. However, we are interested in a subgraph Gi.n of G;.4 that sheds light on ...

A family of arc-transitive graphs is studied. The vertices of these graphs are ordered pairs of distinct points from a finite projective line, and adjacency is defined in terms of the cross ratio. A uniform description of the graphs is given, their automorphism groups are determined, the problem of isomorphism between graphs in the family is solved, some combinatorial properties are explored, a...

This paper shows the results of an experiment in dialogue segmentation. In this experiment, segmentation was done on a level of analysis similar to adjacency pairs. The method of annotation was somewhat novel: volunteers were invited to participate over the Web, and their responses were aggregated using a simple voting method. Though volunteers received a minimum of training, the aggregated res...

We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity of information lost when pairs of nodes are iteratively merged. We show how this measure is equivalent to standard modularity, but also how it is able to dete...

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable–derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method on a simple example, and discuss the dependence of the reconstruct...

This paper describes an efficient technique for computing a hierarchical representation of the objects contained in a complex 3D scene. First, an adjacency graph keeping the costs of grouping the different pairs of objects in the scene is built. Then the minimum spanning tree (MST) of that graph is determined. A binary clustering tree (BCT) is obtained from the MST. Finally, a merging stage joi...

Simplex Adjacency graphs represent the possible Simplex pivot operations (the edges) between pairs of feasible bases (the nodes) of linear optimization models. These graphs are mainly studied so far in the context of degeneracy. The more general point of view in this paper leads to a number of new results, mainly concerning the connectivity and the feasibility-optimality duality in these graphs...

We introduce a new setting of algorithmic problems in random graphs, studying the minimum number of queries one needs to ask about the adjacency between pairs of vertices of G(n, p) in order to typically find a subgraph possessing a given target property. We show that if p ≥ lnn+ln lnn+ω(1) n , then one can find a Hamilton cycle with high probability after exposing (1+o(1))n edges. Our result i...

Realization of the full benefits of variable p-version finite elements requires the careful construction of prismatic elements in thin sections. This paper presents a procedure to automatically isolate the thin sections using the points on an approximate medial surface computed by an octree-based algorithm. Using the pairs of triangles associated with medial surface (MS) points, in conjunction ...

Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem. Introduction Set matrices are matrices whose elements are sets. The matrices comprise abilities of data storing and processing. That makes them a promising combinatorial structure. To prove the concept, this work applies the matrices to the path/cycle problem, see [1, 2, 3, 4, 5, 6, 7, 9, ...