scholarly journals The maximum average connectivity among all orientations of a graph

2021 ◽  
Author(s):  
Rocío M. Casablanca ◽  
Peter Dankelmann ◽  
Wayne Goddard ◽  
Lucas Mol ◽  
Ortrud Oellermann
Keyword(s):  
Average Connectivity

scholarly journals Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

2010 ◽  
Vol 368 (1933) ◽  
pp. 5583-5596 ◽  
Author(s):  
Rudolf Hanel ◽  
Manfred Pöchacker ◽  
Stefan Thurner
Keyword(s):  
Regulatory Networks ◽  
Nonlinear Models ◽  
Reaction Network ◽  
Interaction Network ◽  
Genetic Regulatory Networks ◽  
Frequency Distributions ◽  
Average Connectivity ◽  
Edge Of Chaos ◽  
Oscillating Solutions ◽  
Dynamical Properties

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems , their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network , and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

scholarly journals The average connectivity of a graph

2002 ◽  
Vol 252 (1-3) ◽  
pp. 31-45 ◽  
Author(s):  
Lowell W. Beineke ◽  
Ortrud R. Oellermann ◽  
Raymond E. Pippert
Keyword(s):  
Average Connectivity

A local average connectivity-based method for identifying essential proteins from the network level

2011 ◽  
Vol 35 (3) ◽  
pp. 143-150 ◽  
Author(s):  
Min Li ◽  
Jianxin Wang ◽  
Xiang Chen ◽  
Huan Wang ◽  
Yi Pan
Keyword(s):  
Essential Proteins ◽  
Average Connectivity ◽  
Local Average

scholarly journals Average connectivity and average edge-connectivity in graphs

2013 ◽  
Vol 313 (20) ◽  
pp. 2232-2238 ◽  
Author(s):  
Jaehoon Kim ◽  
Suil O
Keyword(s):  
Edge Connectivity ◽  
Average Connectivity

scholarly journals Bounds on the average connectivity of a graph

2003 ◽  
Vol 129 (2-3) ◽  
pp. 305-318 ◽  
Author(s):  
Peter Dankelmann ◽  
Ortrud R. Oellermann
Keyword(s):  
Average Connectivity

scholarly journals Connectivity and Wiener Index of Fuzzy Incidence Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-7 ◽  
Author(s):  
Juanyan Fang ◽  
Irfan Nazeer ◽  
Tabasam Rashid ◽  
Jia-Bao Liu
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Average Connectivity

Connectivity is a key theory in fuzzy incidence graphs FIGs . In this paper, we introduced connectivity index CI , average connectivity index ACI , and Wiener index WI of FIGs . Three types of nodes including fuzzy incidence connectivity enhancing node FICEN , fuzzy incidence connectivity reducing node FICRN , and fuzzy incidence connectivity neutral node FICNN are also discussed in this paper. A correspondence between WI and CI of a FIG is also computed.

scholarly journals On average connectivity of the strong product of graphs

2013 ◽  
Vol 161 (18) ◽  
pp. 2795-2801
Author(s):  
E. Abajo ◽  
R.M. Casablanca ◽  
A. Diánez ◽  
P. García-Vázquez
Keyword(s):  
Average Connectivity ◽  
Strong Product ◽  
Product Of Graphs

scholarly journals The average connectivity of a digraph

2004 ◽  
Vol 140 (1-3) ◽  
pp. 143-153 ◽  
Author(s):  
Michael A. Henning ◽  
Ortrud R. Oellermann
Keyword(s):  
Average Connectivity
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