381 research outputs found
Line graphs and -geodesic transitivity
For a graph , a positive integer and a subgroup G\leq
\Aut(\Gamma), we prove that is transitive on the set of -arcs of
if and only if has girth at least and is
transitive on the set of -geodesics of its line graph. As applications,
we first prove that the only non-complete locally cyclic -geodesic
transitive graphs are the complete multipartite graph and the
icosahedron. Secondly we classify 2-geodesic transitive graphs of valency 4 and
girth 3, and determine which of them are geodesic transitive
Descriptive Analysis of Characteristics: A Case Study of a Phone Call Network Graph
Nowadays, systematic collection of data has necessitated a detailed statistical analysis as a necessary tool to make a mathematical characterization of them with the purpose of gathering information about the present or the future. Our aim in this paper is to analyze a landline phone call network graph from the perspective of descriptive analysis. We explore the characteristics and structural properties of the network graph constructed using an anonymous collection of data gathered from a Call Data Records of a telecommunication operator center located in south of Albania. The R statistical computing platform is used for network graph analysis
Topics in social network analysis and network science
This chapter introduces statistical methods used in the analysis of social
networks and in the rapidly evolving parallel-field of network science.
Although several instances of social network analysis in health services
research have appeared recently, the majority involve only the most basic
methods and thus scratch the surface of what might be accomplished.
Cutting-edge methods using relevant examples and illustrations in health
services research are provided
Information Diffusion on Social Networks
In this thesis we model the diffusion of information on social networks. A game
played on a specific type of graph generator, the iterated local transitivity
model, is examined. We study how the dynamics of the game change as the
graph grows, and the relationship between properties of the game on a graph
initially and properties of the game later in the graph’s development. We
show that, given certain conditions, for the iterated local transitivity model
it is possible to predict the existence of a Nash equilibrium at any point in
the graph’s growth. We give sufficient conditions for the existence of Nash
Equilibria on star graphs, cliques and trees. We give some results on potential
games on the iterated local transitivity model.
Chapter 2 provides an introduction to graph properties, and describes various
early graph models. Chapter 3 describes some models for online social
networks, and introduces the iterated local transitivity model which we use
later in the thesis. In Chapter 4 various models for games played on networks
are examined. We study a model for competitive information diffusion on
star graphs, cliques and trees, and we provide conditions for the existence of
Nash Equilibria on these. This model for competitive information diffusion is
studied in detail for the iterated local transitivity model in Chapter 5. We
discuss potential games in Chapter 6 and their existence on the iterated local
transitivity model. We conclude with some suggestions on how to extend and
develop upon the work done in this thesis
Geometric aspects of 2-walk-regular graphs
A -walk-regular graph is a graph for which the number of walks of given
length between two vertices depends only on the distance between these two
vertices, as long as this distance is at most . Such graphs generalize
distance-regular graphs and -arc-transitive graphs. In this paper, we will
focus on 1- and in particular 2-walk-regular graphs, and study analogues of
certain results that are important for distance regular graphs. We will
generalize Delsarte's clique bound to 1-walk-regular graphs, Godsil's
multiplicity bound and Terwilliger's analysis of the local structure to
2-walk-regular graphs. We will show that 2-walk-regular graphs have a much
richer combinatorial structure than 1-walk-regular graphs, for example by
proving that there are finitely many non-geometric 2-walk-regular graphs with
given smallest eigenvalue and given diameter (a geometric graph is the point
graph of a special partial linear space); a result that is analogous to a
result on distance-regular graphs. Such a result does not hold for
1-walk-regular graphs, as our construction methods will show
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