scholarly journals Typical distances in the directed configuration model

2018 ◽  
Vol 28 (3) ◽  
pp. 1739-1792 ◽  
Author(s):  
Pim van der Hoorn ◽  
Mariana Olvera-Cravioto
Keyword(s):  
Configuration Model ◽  
Typical Distances

scholarly journals Typical Distances in Ultrasmall Random Networks

2012 ◽  
Vol 44 (2) ◽  
pp. 583-601 ◽  
Author(s):  
Steffen Dereich ◽  
Christian Mönch ◽  
Peter Mörters
Keyword(s):  
Power Law ◽  
Preferential Attachment ◽  
Shortest Paths ◽  
Giant Component ◽  
Configuration Model ◽  
Random Networks ◽  
Power Law Exponent ◽  
Extra Factor ◽  
Typical Distances

We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1))log log N / (-log(τ − 2)), where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.

scholarly journals Typical Distances in Ultrasmall Random Networks

2012 ◽  
Vol 44 (02) ◽  
pp. 583-601 ◽  
Author(s):  
Steffen Dereich ◽  
Christian Mönch ◽  
Peter Mörters
Keyword(s):  
Power Law ◽  
Preferential Attachment ◽  
Shortest Paths ◽  
Giant Component ◽  
Configuration Model ◽  
Random Networks ◽  
Power Law Exponent ◽  
Extra Factor ◽  
Typical Distances

We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 +o(1))log logN/ (-log(τ − 2)), whereNdenotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.

The configuration model

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Degree Sequence ◽  
Graph Model ◽  
Network Models ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Configuration Model ◽  
Bipartite Networks ◽  
Small Component ◽  
Random Graph Model ◽  
Average Size

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a number of basic properties are derived, including the probability of an edge, the expected number of multiedges, the excess degree distribution, the friendship paradox, and the clustering coefficient. This is followed by derivations of some more advanced properties including the condition for the existence of a giant component, the size of the giant component, the average size of a small component, and the expected diameter. Generating function methods for network models are also introduced and used to perform some more advanced calculations, such as the calculation of the distribution of the number of second neighbors of a node and the complete distribution of sizes of small components. The chapter ends with a brief discussion of extensions of the configuration model to directed networks, bipartite networks, networks with degree correlations, networks with high clustering, and networks with community structure, among other possibilities.

Masers as probes of the gas dynamics close to forming high-mass stars

2017 ◽  
Vol 13 (S336) ◽  
pp. 201-206 ◽  
Author(s):  
Luca Moscadelli ◽  
Alberto Sanna ◽  
Ciriaco Goddi
Keyword(s):  
Gas Dynamics ◽  
Very Long Baseline Interferometry ◽  
High Mass ◽  
Powerful Technique ◽  
Long Baseline ◽  
Vlbi Observations ◽  
Massive Forming ◽  
Typical Distances ◽  
New Generation ◽  
Better Than

AbstractImaging the inner few 1000 AU around massive forming stars, at typical distances of several kpc, requires angular resolutions of better than 0″.1. Very Long Baseline Interferometry (VLBI) observations of interstellar molecular masers probe scales as small as a few AU, whereas (new-generation) centimeter and millimeter interferometers allow us to map scales of the order of a few 100 AU. Combining these informations all together, it presently provides the most powerful technique to trace the complex gas motions in the proto-stellar environment. In this work, we review a few compelling examples of this technique and summarize our findings.

scholarly journals Distributed Thermal Energy Storage Configuration of an Urban Electric and Heat Integrated Energy System Considering Medium Temperature Characteristics

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2924
Author(s):  
Wei Wei ◽  
Yusong Guo ◽  
Kai Hou ◽  
Kai Yuan ◽  
Yi Song ◽  
...  
Keyword(s):  
Energy Storage ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Internal Heat ◽  
Configuration Model ◽  
Electric Heater ◽  
Heat Network ◽  
Release Process ◽  
Medium Temperature ◽  
Temperature Characteristics

Distributed thermal energy storage (DTES) provides specific opportunities to realize the sustainable and economic operation of urban electric heat integrated energy systems (UEHIES). However, the construction of the theory of the model and the configuration method of thermal storage for distributed application are still challenging. This paper analyzes the heat absorption and release process between the DTES internal heat storage medium and the heat network transfer medium, refines the relationship between heat transfer power and temperature characteristics, and establishes a water thermal energy storage and electric heater phase change thermal energy storage model, considering medium temperature characteristics. Combined with the temperature transmission delay characteristics of a heat network, a two-stage optimal configuration model of DTES for UEHIES is proposed. The results show that considering the temperature characteristics in the configuration method can accurately reflect the performance of DTES, enhance wind power utilization, improve the operation efficiency of energy equipment, and reduce the cost of the system.

scholarly journals X-Ray Sources in Close Binary Systems

1974 ◽  
Vol 3 ◽  
pp. 89-107
Author(s):  
M. J. Rees
Keyword(s):  
Binary Systems ◽  
Close Binary ◽  
Rapid Variability ◽  
X Ray ◽  
Close Binary Systems ◽  
General Order ◽  
Typical Distances ◽  
Astronomical Research ◽  
Orbital Periods ◽  
Galactic Sources

The discovery by Giacconi and his colleagues of variable X-ray sources in close binary systems certainly ranks as one of the highlights of astronomical research during the last 3 years. These remarkable objects have already been extensively studied, by optical and radio observations as well as in the X-ray band; and they seem likely to prove as significant and far-reaching in their implications as pulsars.The ‘Third Uhuru Catalogue’ (Giacconi et al., 1973a) contains about 160 sources, of which about 100 lie in our Galaxy. Their distribution over the sky (together with other arguments) suggests that these sources have luminosities of the general order 1036–1038 erg s−1, and that their typical distances are ˜ 10kpc. These galactic sources generally display rapid variability. Little else is known about most of them, but they are probably of the same general class as systems such as Her X1, Cen X3, Cyg X1 and Cyg X3. These sources have been investigated in detail, and in all cases one infers a system where the X-ray source is orbiting around a relatively ordinary star. Six sources have been optically identified, and there are some others whose binary nature is established by the occurrence of an X-ray eclipse. Orbital periods range from 4.8 h (Cyg X3) up to ˜ 10 days.

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