Many natural, physical and social networks commonly exhibit power-law degree distributions. In this paper, we discover previously unreported asymmetrical patterns in the degree distributions of incoming and outgoing links in the investigation of large-scale industrial networks, and provide interpretations. In industrial networks, nodes are firms and links are directed supplier-customer relation...

Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident...

A vertex x in a tournament T is called a king if for every vertex y of T there is a directed path from x to y of length at most 2. It is not hard to show that every vertex of maximum out-degree in a tournament is a king. However, tournaments may have kings which are not vertices of maximum out-degree. A binary inquiry asks for the orientation of the edge between a pair of vertices and receives ...

This paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling. More specifically, our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems, one for each ordered pair of classes. The corresponding classifiers are trained on the relevant...

The bisimulation problem for equational graphs of finite out-degree is shown to be decidable. We reduce this problem to the η-bisimulation problem for deterministic rational (vectors of) boolean series on the alphabet of a dpda M. We then exhibit a complete formal system for deducing equivalent pairs of such vectors.

00 1 + L: If some mild conditions are satisfied, then Y n "'-' c( cp( T ) / T t . n -3 /2 1 where TCP' (T) cp( T). We say that a node v in a rooted tree has out-degree k if v is incident with k edges that lead away from the root of Tn. Our object here is to the behaviour of the maximum ~ ~(Tn) of trees in F. After describing briefly in §2 the ;:"'A~vL .u,,,,,-,ufamilies of trees we shall be con...

The present research aimed to study the application of Fuzzy logic in social science research. In this regard, based on two variables, Social Capital and Quality of Life, the degree of Tehran’s membership in the set of social development was studied using FSQCA software.This research was an applied and descriptive research methodologically; and extensive in quantitative...