An exact algorithm to find a maximum weight clique in a weighted undirected graph by Kati Rozman, An Ghysels, Dušanka Janežič, Janez Konc

“…Our findings reveal a remarkable improvement in computational speed when compared to existing algorithms, particularly evident in the case of high-density random graphs and DIMACS graphs, where our newly developed algorithm outperforms existing alternatives by several orders of magnitude. …”
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Starling: Introducing a mesoscopic scale with Confluence for Graph Clustering by Bruno Gaume

“…These comparisons are done, on the one hand with artificial Graphs (a) Random Graphs and (b) a classical Graphs Clustering Benchmark, and on the other hand with (c) Terrain-Graphs gathered from real data. …”
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Fast Approximate Convex Hull Construction in Networks via Node Embedding by Dmitrii Gavrilev, Ilya Makarov

“…It aids in distinguishing between real-world networks and random graphs. One possible application is recommending new connections in a collaborative network by searching for them in the so-called convex hull, which is a minimal subgraph containing all the shortest paths between its nodes. …”
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Starling: Introducing a mesoscopic scale with Confluence for Graph Clustering. by Bruno Gaume

“…These comparisons are done, on the one hand with artificial Graphs (a) Random Graphs and (b) a classical Graphs Clustering Benchmark, and on the other hand with (c) Terrain-Graphs gathered from real data. …”
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Linear stability analysis of large dynamical systems on random directed graphs by Izaak Neri, Fernando Lucas Metz

“…We corroborate analytical results for infinitely large graphs with numerical experiments on random graphs of finite size. We discuss how the presented theory can be extended to graphs with diagonal disorder and to graphs that contain nondirected links. …”
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Evolutionary Games of Multiplayer Cooperation on Graphs. by Jorge Peña, Bin Wu, Jordi Arranz, Arne Traulsen

“…Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.…”
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Advanced Wireless Communications and Internet : Future Evolving Technologies / by Glisic, Savo G., author 315614

“…Furthermore, a number of methodologies for maintaining the network connectivity, by using tools ranging from genetic algorithms to stochastic geometry and random graphs theory, and a discussion on percolation and connectivity, are also offered. …”

Local Statistic With Dynamic Vertex Selection for Change-Point Detection in Stochastic Block Networks by Yanping Zhao, Bo Wang, Mingan Luan, Fengye Hu

“…In this paper, we consider the stochastic block model of random graphs, and study the change-point detection regarding to the scenario that after a change-point, the connectivity of subnetworks becomes denser or sparser while the membership of nodes also changes. …”
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A curve shaped description of large networks, with an application to the evaluation of network models. by Xianchuang Su, Xiaogang Jin, Yong Min, Linjian Mo, Jiangang Yang

“…After deriving the expressions of the curves of the random graphs and a small-world-like network, we found that the curves possess a number of network properties together, including the size of the giant component and the local clustering. …”
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Local bow-tie structure of the web by Yuji Fujita, Yuichi Kichikawa, Yoshi Fujiwara, Wataru Souma, Hiroshi Iyetomi

“…To quantify the mutual connectivity among such local bow-tie, we define a quantity to measure how a local bow-tie connects to others in comparison with random graphs. We found that there are striking difference between the WWW and other social and artificial networks including a million firms’ nationwide supply chain network in Japan and thousands of symbols’ dependency in the programming language of Emacs LISP, in which a global bow-tie exits. …”
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A Social Network Approach to the Dual Aspect of Moral Competence by Silvio Salej Higgins, Guillermo Vega Sanabria, Patrícia Unger Raphael Bataglia, Erick Fontenele Gonçalves, Lavínia Ferreira da Silva Carmo

“…Following this, a sociometric generator regarding relationships of friendship and collaboration in social networks was applied, and several Exponential Random Graphs Models (ERGMs), with the MCT-xt score as an exogenous effect and predictor of these relationships, were utilized. …”
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Descendant distributions for the impact of mutant contagion on networks by Jonas S. Juul, Steven H. Strogatz

“…We find that the tail of the distribution decays as d^{−2} for complete graphs, random graphs, small-world networks, networks with block-like structure, and other infinite-dimensional networks. …”
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All-to-all communication with low communication cost by Wan, Jun (Computer scientist) Massachusetts Institute of Technology

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Robust object exploration and detection by Velez, Javier J

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Similarity-based parameter transferability in the quantum approximate optimization algorithm by Alexey Galda, Alexey Galda, Eesh Gupta, Eesh Gupta, Jose Falla, Jose Falla, Xiaoyuan Liu, Xiaoyuan Liu, Danylo Lykov, Yuri Alexeev, Ilya Safro

“…We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. …”
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A New Method of Quantifying the Complexity of Fractal Networks by Matej Babič, Dragan Marinković, Miha Kovačič, Branko Šter, Michele Calì

“…In the context of network theory, a complex network is a graph with nontrivial topological features—features that do not occur in simple networks, such as lattices or random graphs, but often occur in graphs modeling real systems. …”
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Graph Burning: Mathematical Formulations and Optimal Solutions by Jesús García-Díaz, Lil María Xibai Rodríguez-Henríquez, Julio César Pérez-Sansalvador, Saúl Eduardo Pomares-Hernández

“…We empirically compared the proposed formulations using random graphs and off-the-shelf optimization software. …”
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Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity by C. A. Trugenberger

“…Abstract Combinatorial quantum gravity is governed by a discrete Einstein-Hilbert action formulated on an ensemble of random graphs. There is strong evidence for a second-order quantum phase transition separating a random phase at strong coupling from an ordered, geometric phase at weak coupling. …”
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Credit Risk Contagion and Systemic Risk on Networks by Marina Dolfin, Damian Knopoff, Michele Limosani, Maria Gabriella Xibilia

“…We perform numerical simulations intended to explore the roles played by two different network structures on the long-term behavior of assets affected by systemic risk in order to analyze the effect of the topology of the underlying network structure on the spreading of systemic risk on the structure. Random graphs, i.e., the Erdös−Rényi model, are considered “benchmark” network structures while core-periphery structures are often indicated in the literature as idealized structures, although they are able to capture interesting, specific features of real-world financial networks. …”
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From Spin Glasses to Negative-Weight Percolation by Alexander K. Hartmann, Oliver Melchert, Christoph Norrenbrock

“…This includes the study of percolation transitions in dimension from <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> up to and beyond the upper critical dimension <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>d</mi> <mi>u</mi> </msub> <mo>=</mo> <mn>6</mn> </mrow> </semantics> </math> </inline-formula>, also for random graphs. It is shown that NWP is in a different universality class than standard percolation. …”
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