In contrast to previous analyses of the atom of kinship as a signed graph in which the ideal combinations of relations are predicted from the theory of structural balance, this article suggests a ...

We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the ...

Using this definition of path, OP, you must realize that there may be exponentially (in the number of vertices + edges in the graph) many paths between two vertices (even in simple graphs).

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

Graph theory, a nearly 300-year-old discipline considered an element of discrete mathematics, is used to model many types of relationships and processes in physical, biological, social and information ...

Chayes and Borgs's prior university labors on graph theory and phase transitions have been of some use to the enterprise. Since they joined Microsoft, the World Wide Web has come into its own.

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...