84 research outputs found
Giant Clusters in Random Ad Hoc Networks
The present paper introduces ad hoc communication networks as examples of
large scale real networks that can be prospected by statistical means. A
description of giant cluster formation based on the single parameter of node
neighbor numbers is given along with the discussion of some asymptotic aspects
of the giant cluster sizes.Comment: 6 pages, 5 figures; typos and correction
Markov Chain Methods For Analyzing Complex Transport Networks
We have developed a steady state theory of complex transport networks used to
model the flow of commodity, information, viruses, opinions, or traffic. Our
approach is based on the use of the Markov chains defined on the graph
representations of transport networks allowing for the effective network
design, network performance evaluation, embedding, partitioning, and network
fault tolerance analysis. Random walks embed graphs into Euclidean space in
which distances and angles acquire a clear statistical interpretation. Being
defined on the dual graph representations of transport networks random walks
describe the equilibrium configurations of not random commodity flows on
primary graphs. This theory unifies many network concepts into one framework
and can also be elegantly extended to describe networks represented by directed
graphs and multiple interacting networks.Comment: 26 pages, 4 figure
Pseudofractal Scale-free Web
We find that scale-free random networks are excellently modeled by a
deterministic graph. This graph has a discrete degree distribution (degree is
the number of connections of a vertex) which is characterized by a power-law
with exponent . Properties of this simple structure are
surprisingly close to those of growing random scale-free networks with
in the most interesting region, between 2 and 3. We succeed to find exactly and
numerically with high precision all main characteristics of the graph. In
particular, we obtain the exact shortest-path-length distribution. For the
large network () the distribution tends to a Gaussian of width
centered at . We show that the
eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail
with exponent .Comment: 5 pages, 3 figure
Spectra of complex networks
We propose a general approach to the description of spectra of complex
networks. For the spectra of networks with uncorrelated vertices (and a local
tree-like structure), exact equations are derived. These equations are
generalized to the case of networks with correlations between neighboring
vertices. The tail of the density of eigenvalues at large
is related to the behavior of the vertex degree distribution
at large . In particular, as , . We propose a simple approximation, which enables us to
calculate spectra of various graphs analytically. We analyse spectra of various
complex networks and discuss the role of vertices of low degree. We show that
spectra of locally tree-like random graphs may serve as a starting point in the
analysis of spectral properties of real-world networks, e.g., of the Internet.Comment: 10 pages, 4 figure
Correlation between centrality metrics and their application to the opinion model
In recent decades, a number of centrality metrics describing network
properties of nodes have been proposed to rank the importance of nodes. In
order to understand the correlations between centrality metrics and to
approximate a high-complexity centrality metric by a strongly correlated
low-complexity metric, we first study the correlation between centrality
metrics in terms of their Pearson correlation coefficient and their similarity
in ranking of nodes. In addition to considering the widely used centrality
metrics, we introduce a new centrality measure, the degree mass. The m order
degree mass of a node is the sum of the weighted degree of the node and its
neighbors no further than m hops away. We find that the B_{n}, the closeness,
and the components of x_{1} are strongly correlated with the degree, the
1st-order degree mass and the 2nd-order degree mass, respectively, in both
network models and real-world networks. We then theoretically prove that the
Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is
larger than that between x_{1} and a lower order degree mass. Finally, we
investigate the effect of the inflexible antagonists selected based on
different centrality metrics in helping one opinion to compete with another in
the inflexible antagonists opinion model. Interestingly, we find that selecting
the inflexible antagonists based on the leverage, the B_{n}, or the degree is
more effective in opinion-competition than using other centrality metrics in
all types of networks. This observation is supported by our previous
observations, i.e., that there is a strong linear correlation between the
degree and the B_{n}, as well as a high centrality similarity between the
leverage and the degree.Comment: 20 page
Mixing patterns in networks
We study assortative mixing in networks, the tendency for vertices in
networks to be connected to other vertices that are like (or unlike) them in
some way. We consider mixing according to discrete characteristics such as
language or race in social networks and scalar characteristics such as age. As
a special example of the latter we consider mixing according to vertex degree,
i.e., according to the number of connections vertices have to other vertices:
do gregarious people tend to associate with other gregarious people? We propose
a number of measures of assortative mixing appropriate to the various mixing
types, and apply them to a variety of real-world networks, showing that
assortative mixing is a pervasive phenomenon found in many networks. We also
propose several models of assortatively mixed networks, both analytic ones
based on generating function methods, and numerical ones based on Monte Carlo
graph generation techniques. We use these models to probe the properties of
networks as their level of assortativity is varied. In the particular case of
mixing by degree, we find strong variation with assortativity in the
connectivity of the network and in the resilience of the network to the removal
of vertices.Comment: 14 pages, 2 tables, 4 figures, some additions and corrections in this
versio
Measurements of Higgs boson production cross sections and couplings in the diphoton decay channel at root s=13 TeV
Measurements of Higgs boson production cross sections and couplings in events where the Higgs boson decays into a pair of photons are reported. Events are selected from a sample of proton-proton collisions at root s = 13TeV collected by the CMS detector at the LHC from 2016 to 2018, corresponding to an integrated luminosity of 137 fb(-1). Analysis categories enriched in Higgs boson events produced via gluon fusion, vector boson fusion, vector boson associated production, and production associated with top quarks are constructed. The total Higgs boson signal strength, relative to the standard model (SM) prediction, is measured to be 1.12 +/- 0.09. Other properties of the Higgs boson are measured, including SM signal strength modifiers, production cross sections, and its couplings to other particles. These include the most precise measurements of gluon fusion and vector boson fusion Higgs boson production in several different kinematic regions, the first measurement of Higgs boson production in association with a top quark pair in five regions of the Higgs boson transverse momentum, and an upper limit on the rate of Higgs boson production in association with a single top quark. All results are found to be in agreement with the SM expectations.Peer reviewe
- …