scholarly journals Simple graph models of information spread in finite populations

2015 ◽  
Vol 2 (5) ◽  
pp. 150028 ◽  
Author(s):  
Burton Voorhees ◽  
Bergerud Ryder
Keyword(s):  
Information Diffusion ◽  
Transition Probability ◽  
Bipartite Graphs ◽  
Hitting Times ◽  
Antisymmetric Part ◽  
Directional Bias ◽  
Single Link ◽  
Fixation Probabilities ◽  
Circular Flows ◽  
Graph Parameters

We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call ‘single-link’ graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the non-zero eigenvalues of the antisymmetric part of the Laplacian and another measure is found for cycles as the value of the transition probability for which hitting times going in either direction of the cycle are equal. A generalization of circular flow graphs is used to illustrate the possibility of tuning edge weights to match pre-specified values for graph parameters; in particular, we show that generalizations of circular flows can be tuned to have fixation probabilities equal to the Moran probability for a complete graph by tuning vertex temperature profiles. Finally, single-link graphs are introduced as an example of a graph involving a bottleneck in the connection between two components and these are compared to the partial bipartite graphs.

scholarly journals Energy of extended bipartite double graphs

2021 ◽  
Vol 87 (3) ◽  
pp. 653-660
Author(s):  
Harishchandra S. Ramane ◽  
◽  
B. Parvathalu ◽  
K. Ashoka
Keyword(s):  
Bipartite Graphs ◽  
Exact Relation ◽  
The Absolute ◽  
Graph Parameters

The energy of a graph is the sum of the absolute values of its eigenvalues. In this article, an exact relation between the energy of extended bipartite double graph and the energy of a graph together with some other graph parameters is given. As a consequence, equienergetic, borderenergetic, orderenergetic and non-hyperenergetic extended bipartite double graphs are presented. The obtained results generalize the existing results on equienergetic bipartite graphs.

scholarly journals A Markov model for seismic hazard analysis along the Hellenic subduction Zone (Greece)

2016 ◽  
Vol 47 (3) ◽  
pp. 1376
Author(s):  
I. Votsi ◽  
G. Tsaklidis ◽  
N. Limnios ◽  
E. Papadimitriou ◽  
F. Vallianatos
Keyword(s):  
Seismic Hazard ◽  
Markov Model ◽  
Subduction Zone ◽  
Hazard Analysis ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Point Of View ◽  
Hitting Times ◽  
Stochastic Representation ◽  
Hellenic Subduction Zone

A homogeneous finite–state discrete–time Markov model is applied for the earthquake occurrence in the Hellenic Subduction Zone (Greece), a region accommodating high seismic activity, being a key structure from a seismotectonic point of view. An attempt is made to provide a stochastic representation of the earthquake process and to assess the seismic hazard through the application of the Markov model. The model is applied on a complete data sample comprising strong () eart  h-quakes that occurred in the study area since 1911 up to present. The continuous magnitude scale is divided into appropriate intervals to specify discrete states of the model. As the stochastic behavior of the model is governed by its transition probability matrix, we firstly estimate its well–known maximum likelihood estimator. The estimation of the transition probability matrix leads to the estimation of important indicators of the Markov chain, including hitting times and failure rate functions. The   mean number of steps for the first occurrence of an anticipated earthquake (belonging to the class with the stronger events, which we are more interested in) is estimated along with its variance. In a next step, we calculate the confidence interval of the   aforementioned estimators.

scholarly journals On Color Energy of Few Classes of Bipartite Graphs and Corresponding Color Complements

1970 ◽  
Vol 8 (1) ◽  
pp. 7-14
Author(s):  
Prajakta Bharat Joshi ◽  
Mayamma Joseph
Keyword(s):  
Chromatic Number ◽  
Domination Number ◽  
Bipartite Graphs ◽  
Subject Classification ◽  
Proper Coloring ◽  
Colored Graph ◽  
Ams Subject Classification ◽  
Graph Parameters

For a given colored graph G, the color energy is defined as Ec(G) = Σλi, for i = 1, 2,…., n; where λi is a color eigenvalue of the color matrix of G, Ac (G) with entries as 1, if both the corresponding vertices are neighbors and have different colors; -1, if both the corresponding vertices are not neighbors and have same colors and 0, otherwise. In this article, we study color energy of graphs with proper coloring and L (h, k)-coloring. Further, we examine the relation between Ec(G) with the corresponding color complement of a given graph G and other graph parameters such as chromatic number and domination number. AMS Subject Classification: 05C15, 05C50

Bipartite Graphs and their Applications

1998 ◽  
Author(s):  
Armen S. Asratian ◽  
Tristan M. J. Denley ◽  
Roland Häggkvist
Keyword(s):  
Bipartite Graphs

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Regional household poverty and mobility analysis – a transition probability approach

2020 ◽  
Vol 63 (3) ◽  
pp. 286-302
Author(s):  
Damian Mowczan ◽  
Keyword(s):  
Transition Probability ◽  
General Level ◽  
Transition Matrices ◽  
Equivalent Unit ◽  
Central Statistical ◽  
Per Capita ◽  
Probability Matrices ◽  
General Mobility ◽  
One Year ◽  
The One

The main objective of this paper was to estimate and analyse transition-probability matrices for all 16 of Poland’s NUTS-2 level regions (voivodeship level). The analysis is conducted in terms of the transitions among six expenditure classes (per capita and per equivalent unit), focusing on poverty classes. The period of analysis was two years: 2015 and 2016. The basic aim was to identify both those regions in which the probability of staying in poverty was the highest and the general level of mobility among expenditure classes. The study uses a two-year panel sub-sample of unidentified unit data from the Central Statistical Office (CSO), specifically the data concerning household budget surveys. To account for differences in household size and demographic structure, the study used expenditures per capita and expenditures per equivalent unit simultaneously. To estimate the elements of the transition matrices, a classic maximum-likelihood estimator was used. The analysis used Shorrocks’ and Bartholomew’s mobility indices to assess the general mobility level and the Gini index to assess the inequality level. The results show that the one-year probability of staying in the same poverty class varies among regions and is lower for expenditures per equivalent units. The highest probabilities were identified in Podkarpackie (expenditures per capita) and Opolskie (expenditures per equivalent unit), and the lowest probabilities in Kujawsko-Pomorskie (expenditures per capita) and Małopolskie (expenditures per equivalent unit). The highest level of general mobility was noted in Małopolskie, for both categories of expenditures.

Sign in / Sign up

Export Citation Format

Share Document