A tree must be acyclic, meaning it should not contain any cycles. A cycle is a path that starts and ends at the same vertex without repeating edges. The presence of a cycle indicates that there are ...

Self-organized structures can spontaneously emerge from a complex sea of microscopic, interacting constituents. This is a widespread observation in nature, now accepted as a paradigmatic concept in ...

Journal of Applied Probability, Vol. 29, No. 3 (Sep., 1992), pp. 745-749 (5 pages) The dependence of coincidence of the global, local and pairwise Markov properties on the underlying undirected graph ...

A real variate is defined for the ordered pairs of nodes in a finite graph. We consider the problem of estimating the total of the variate values from the information provided by a node sample. The ...