scholarly journals Network comparison and the within-ensemble graph distance

2020 ◽  
Vol 476 (2243) ◽  
pp. 20190744
Author(s):  
Harrison Hartle ◽  
Brennan Klein ◽  
Stefan McCabe ◽  
Alexander Daniels ◽  
Guillaume St-Onge ◽  
...  
Keyword(s):  
Ad Hoc ◽  
Preferential Attachment ◽  
Network Models ◽  
Distance Measures ◽  
Configuration Model ◽  
Graph Distance ◽  
Network Comparison ◽  
Random Geometric Graphs ◽  
Graph Distances ◽  
New Framework

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years, a multitude of diverse, ad hoc solutions to this problem have been introduced. Here, we propose that simple and well-understood ensembles of random networks—such as Erdős–Rényi graphs, random geometric graphs, Watts–Strogatz graphs, the configuration model and preferential attachment networks—are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

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.

scholarly journals Likelihood-based approach to discriminate mixtures of network models that vary in time

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Naomi A. Arnold ◽  
Raul J. Mondragón ◽  
Richard G. Clegg
Keyword(s):  
Network Model ◽  
Change Point ◽  
Network Science ◽  
Preferential Attachment ◽  
Network Models ◽  
Explanatory Models ◽  
Growth Mechanisms ◽  
Artificial Data ◽  
Network Growth ◽  
Over Time

AbstractDiscriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms such as preferential attachment and triangle closure, with a wealth of explanatory models based on these. These models are deliberately simple, commonly with the network growing according to a constant mechanism for its lifetime, to allow for analytical results. We use a likelihood-based framework on artificial data where the network model changes at a known point in time and demonstrate that we can recover the change point from analysis of the network. We then use real datasets and demonstrate how our framework can show the changing importance of network growth mechanisms over time.

scholarly journals Friendship paradox in growth networks: analytical and empirical analysis

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sergei P. Sidorov ◽  
Sergei V. Mironov ◽  
Alexey A. Grigoriev
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Empirical Studies ◽  
Mean Field ◽  
Network Models ◽  
Average Degree ◽  
Closure Model ◽  
Triadic Closure ◽  
Attachment Mechanism ◽  
Over Time

AbstractMany empirical studies have shown that in social, citation, collaboration, and other types of networks in real world, the degree of almost every node is less than the average degree of its neighbors. This imbalance is well known in sociology as the friendship paradox and states that your friends are more popular than you on average. If we introduce a value equal to the ratio of the average degree of the neighbors for a certain node to the degree of this node (which is called the ‘friendship index’, FI), then the FI value of more than 1 for most nodes indicates the presence of the friendship paradox in the network. In this paper, we study the behavior of the FI over time for networks generated by growth network models. We will focus our analysis on two models based on the use of the preferential attachment mechanism: the Barabási–Albert model and the triadic closure model. Using the mean-field approach, we obtain differential equations describing the dynamics of changes in the FI over time, and accordingly, after obtaining their solutions, we find the expected values of this index over iterations. The results show that the values of FI are decreasing over time for all nodes in both models. However, for networks constructed in accordance with the triadic closure model, this decrease occurs at a much slower rate than for the Barabási–Albert graphs. In addition, we analyze several real-world networks and show that their FI distributions follow a power law. We show that both the Barabási–Albert and the triadic closure networks exhibit the same behavior. However, for networks based on the triadic closure model, the distributions of FI are more heavy-tailed and, in this sense, are closer to the distributions for real networks.

scholarly journals Self-organizing topology for energy-efficient ad-hoc communication networks of mobile devices

2020 ◽  
Author(s):  
Indushree Banerjee ◽  
Martijn Warnier ◽  
Frances M. T Brazier
Keyword(s):  
Communication Network ◽  
Mobile Devices ◽  
Communication Networks ◽  
Energy Efficient ◽  
Ad Hoc ◽  
Preferential Attachment ◽  
Scale Free ◽  
Simulated Environment ◽  
Adaptive Topology ◽  
Hoc Networks

Abstract When physical communication network infrastructures fail, infrastructure-less communication networks such as mobile ad-hoc networks (MANET), can provide an alternative. This, however, requires MANETs to be adaptable to dynamic contexts characterized by the changing density and mobility of devices and availability of energy sources. To address this challenge, this paper proposes a decentralized context-adaptive topology control protocol. The protocol consists of three algorithms and uses preferential attachment based on the energy availability of devices to form a loop-free scale-free adaptive topology for an ad-hoc communication network. The proposed protocol has a number of advantages. First, it is adaptive to the environment, hence applicable in scenarios where the number of participating mobile devices and their availability of energy resources is always changing. Second, it is energy-efficient through changes in the topology. This means it can be flexibly be combined with different routing protocols. Third, the protocol requires no changes on the hardware level. This means it can be implemented on all current phones, without any recalls or investments in hardware changes. The evaluation of the protocol in a simulated environment confirms the feasibility of creating and maintaining a self-adaptive ad-hoc communication network, consisting of multitudes of mobile devices for reliable communication in a dynamic context.

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.

Sensitivity analysis for network observations with applications to inferences of social influence effects

2020 ◽  
pp. 1-26
Author(s):  
Ran Xu ◽  
Kenneth A. Frank
Keyword(s):  
Sensitivity Analysis ◽  
Social Influence ◽  
Preferential Attachment ◽  
Empirical Studies ◽  
Network Models ◽  
Systematic Bias ◽  
Random Measurement Error ◽  
Statistical Inferences ◽  
Sensitivity Analysis Method ◽  
Selection Mechanisms

Abstract The validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.

Historic Sites Archaeology on the Western American Frontier: Theoretical Perspectives and Research Problems

1981 ◽  
Vol 2 (1) ◽  
pp. 67-82 ◽  
Author(s):  
Donald L. Hardesty
Keyword(s):  
Island Biogeography ◽  
Ad Hoc ◽  
Cultural Resource Management ◽  
Western United States ◽  
Historic Sites ◽  
American Frontier ◽  
Integrative Research ◽  
Theoretical Perspectives ◽  
Research Problems ◽  
New Framework

Historic sites archaeology in the western United States is booming but continues to be conducted ad hoc. The demands of assessing significance for cultural resource management purposes suggests that integrative research problems must be identified. One set of such problems emerge from the frontier concept. The use of synecological models from general ecology is proposed as a new framework within which to better understand frontier phenomena. As an illustration, one aspect of Frederick Jackson Turner's “frontier thesis” — the homogenization of frontier behavior — is examined in this light and related to historic sites research. In addition patterns of frontier colonization are studied with models of island biogeography developed by the late Robert MacArthur and E. O. Wilson.

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