Fast GPU-Based Generation of Large Graph Networks From Degree Distributions by Maksudul Alam, Kalyan Perumalla

“…Given an array of desired vertex degrees and number of vertices for each desired degree, our algorithm generates the edges of a random graph that satisfies the input degree distribution. …”
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Presenting a Scale-Free Complex Network with a Persian Language Layered Composition Pattern by Ali Sarabadani, Kheirollah Rahsepar Fard, Sepideh Chehreh

“…Method: A null model of the same size is generated using the Erdos-Renyi random graph for comparison with the Persian network. …”
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Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit. by Michael T Schaub, Jean-Charles Delvenne, Sophia N Yaliraki, Mauricio Barahona

“…Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. …”
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Temporal dynamics of streamflow: application of complex networks by Xudong Han, Bellie Sivakumar, Fitsum M. Woldmeskel, Milena Guerra de Aguilar

“…The results suggest that (1) there are only a few very significant nodes (years) in the annual streamflow network (degree centrality method); (2) the annual streamflow network is not a classical random graph, but may be a small-world network or scale-free network (clustering coefficient method); and (3) the network exhibits a combination of exponential and power-law distribution (degree distribution method). …”
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Formation of trade networks by economies of scale and product differentiation by Chengyuan Han, Malte Schröder, Dirk Witthaut, Philipp C Böttcher

“…Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this article, we establish a model for the emergence of trade networks that is based on rational decisions of individual agents. …”
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Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals. by Olav Stetter, Demian Battaglia, Jordi Soriano, Theo Geisel

“…Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.…”
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Small modifications to network topology can induce stochastic bistable spiking dynamics in a balanced cortical model. by Mark D McDonnell, Lawrence M Ward

“…Directed random graph models frequently are used successfully in modeling the population dynamics of networks of cortical neurons connected by chemical synapses. …”
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Socio-spatial relations observed in the global city network of firms. by Thomas Sigler, Kirsten Martinus, Julia Loginova

“…We then test these by applying an exponential random graph model (ERGM) to explain how each dimension may contribute to cities' embeddedness within the overall network. …”
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A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem by Barak, Boaz, Hopkins, Samuel B., Kothari, Pravesh, Potechin, Aaron, Moitra, Ankur, Kelner, Jonathan Adam

“…We prove that with high probability over the choice of a random graph G from the Erds-Rényi distribution G(n,1/2), the n[superscript o(d)]-time degree d Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least n[superscript 1/2-c(d/log n)1/2] for some constant c > 0. …”
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Giant Component in Random Multipartite Graphs with given Degree Sequences by Gamarnik, David, Misra, Sidhant

“…We use the exploration process of Molloy and Reed Molloy and Reed (1995) to analyze the size of components in the random graph. The main challenges arise due to the multidimensionality of the random processes involved which prevents us from directly applying the techniques from the standard unipartite case. …”
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Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz by Fox, Jacob, Lee, Choongbum, Sudakov, Benny

“…Erd}os and Fajtlowicz further showed by considering a random graph that H(n) cn1=2= log n for some absolute constant c > 0. …”
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Energy-latency tradeoff for in-network function computation in random networks by Balister, Paul, Bollobas, Bela, Anandkumar, Animashree, Willsky, Alan S.

“…The policy is then extended to computation of a general class of functions which decompose according to maximal cliques of a proximity graph such as the k-nearest neighbor graph or the geometric random graph. The modified policy achieves order-optimal energy consumption albeit for a limited range of latency constraints.…”
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Percolation and Connectivity in the Intrinsically Secure Communications Graph by Pinto, Pedro C., Win, Moe Z.

“…The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. …”
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Queueing system topologies with limited flexibility by Tsitsiklis, John N., Xu, Kuang

“…In particular, when d(n) gg ln n , a family of random-graph-based interconnection topologies is (with high probability) capable of stabilizing all admissible arrival rate vectors (under a bounded support assumption), while simultaneously ensuring a diminishing queueing delay, of order ln n/ d(n), as n-> ∞. …”
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Wide-sense stationarity and spectral estimation for generalized graph signal by Jian, Xingchao, Tay, Wee Peng

“…We introduce the notion of joint wide-sense stationarity in this generalized GSP (GGSP) framework, which allows us to characterize a random graph process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. …”
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Friendship based on race or race based on friendship? The co-evoluation of friendships, negative ties and ethnic perceptions in Hungarian school classes by Boda, Z

“…For the analyses, we take a social networks approach, estimating exponential random graph and stochastic actor-oriented models. First, we take a look at the state of racial segregation in friendships and negative ties within communities, and we investigate the dynamic processes that have led to the described state. …”

The formation, structure, and multiplexity of criminal networks by Wood, G

“…Paper two reports the results of a Bayesian Exponential Random Graph Model of Collaborative Tie Formation in a Drug Trafficking Network, which explores the formation of collaborative ties in the trafficking organization, testing whether collaboration is subject to endogenous shared partner effects and homophily effects by subgroup membership and task specialization. …”

Structural complexity of one-dimensional random geometric graphs by Badiu, M-A, Coon, JP

“…The upper bounds in this paper easily extend to the entropy of the labeled random graph model, since this is given by the structural entropy plus a term that accounts for all the permutations of node labels that are possible for a given structure, which is no larger than log2(n!)…”

Stein's method for functional approximations by Kasprzak, M

“…Those are applied to examples coming from queuing theory, random-graph theory, statistics and combinatorics.</p> <p>We firstly look at the motivation for this thesis and an overview of Stein's method. …”

Uniform random planar graphs with degree constraints by Dowden, C

“…Many basic properties of the standard uniform random planar graph $P_{n}$, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set $ { 1,2, ldots, n }$, are now known, and variations on this standard random graph are also attracting interest. Prominent among the work on $P_{n}$ have been asymptotic results for the probability that $P_{n}$ will be connected or contain given components/ subgraphs. …”