Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared...

In the process of compiling a computer programme, we consider the problem of allocating variables to registers within a loop. It can be formulated as a coloring problem in a circular arc graph (intersection graph of a family F of intervals on a circle). We consider the meeting graph of F introduced by Eisenbeis, Lelait and Marmol. Proceedings of the Fifth Workshop on Compilers for Parallel Comp...

We show that higher order epistasis has a substantial impact on evolutionary dynamics by analyzing peaks in the fitness landscapes. There are 193,270,310 fitness graphs, or cube orientations, for 4-locus systems, distributed on 511, 863 isomorphism classes. We identify all fitness graphs with 6 or more peaks. 81 percent of them imply 4-way epistasis, whereas 9 percent of all 4-locus fitness gra...

Three characterizations of quasi-median graphs are proved, for instance, they are partial Hamming graphs without convex house and convexQ 3 such that certain relations on their edge sets coincide. Expansion procedures, weakly 2-convexity, and several relations on the edge set of a graph are essential for these results. Quasisemimedian graphs are characterized which yields an additional characte...

In multi-resolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the gran-ulation of graphs is an important top...

The most frequently used language to represent the semantic graphs is the RDF (W3C standard for meta-modeling). The construction of semantic graphs is a source of numerous errors of interpretation. The processing of large semantic graphs is a limit to the use of semantics in current information systems. The work presented in this paper is part of a new research at the border between two areas: ...

The modularity maximization model proposed by Newman and Girvan for the identification of communities in networks works for general graphs possibly with loops and multiple edges. However, the applications usually correspond to simple graphs. These graphs are compared to a null model where the degree distribution is maintained but edges are placed at random. Therefore, in this null model there w...

Many problems can be cast as statistical inference on an attributed random graph. Our motivation is change detection in communication graphs. We prove that tests based on a fusion of graph-derived and content-derived metadata can be more powerful than those based on graph or content features alone. For some basic attributed random graphmodels, we derive fusion tests from the likelihood ratio. W...

The edit distance is a very simple and natural metric on the space of graphs. In the edit distance problem, we fix a hereditary property of graphs and compute the asymptotically largest edit distance of a graph from the property. This quantity is very difficult to compute directly but in many cases, it can be derived as the maximum of the edit distance function. Szemerédi’s regularity lemma, st...