Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation r, being random in other aspects and preserving the degree sequence. This can be done through Monte Carlo optimization procedures. Meanwhile, when tuning r, other n...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

This paper argues that Mandarin Chinese fills a gap in the typology of comparative constructions in natural language. Beck et al. (2004) proposes that languages may vary in whether or not they allow for degree abstraction, and Kennedy (2007) proposes a distinction between comparative constructions with degree-denoting standards and individual-denoting standards. Based on these parameters, we ex...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

for a nite group g the commutativity degree denote by d(g) and dend: d(g) = jf(x; y)jx; y 2 g; xy = yxgj jgj2 : in [2] authors found commutativity degree for some groups,in this paper we nd commuta- tivity degree for a class of groups that have high nilpontencies.

In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides rigorous framework for estimating complexity system equations via Gröbner bases methods. Our main results include connection between last fall one regularity Castelnuovo–Mumford regularity.