Understanding random-walk dynamical phase coexistence through waiting times by David C. Stuhrmann, Francesco Coghi

“…We illustrate these results through three analytical examples which provide insights into random walks exploring random graphs.…”
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Topology of random $2$-dimensional cubical complexes by Matthew Kahle, Elliot Paquette, Érika Roldán

“…This is a $2$-dimensional analogue of the Burtin and Erdoős–Spencer theorems characterising the connectivity threshold for random graphs on the $1$-skeleton of the n-dimensional cube.…”
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Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies by Francisco W. De Sousa Lima

“…These are investigated on networks, like Apollonian (AN), Barabási–Albert (BA), small-worlds (SW), Voronoi–Delaunay (VD) and Erdös–Rényi (ER) random graphs. The review here is on phase transitions, critical points, exponents and universality classes that are compared to the results obtained for these models on regular square lattices (SL).…”
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U-statistics and random subgraph counts: Multivariate normal approximation via exchangeable pairs and embedding by Reinert, G, Röllin, A

“…Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs.…”

RANDOM SUBGRAPH COUNTS AND U-STATISTICS: MULTIVARIATE NORMAL APPROXIMATION VIA EXCHANGEABLE PAIRS AND EMBEDDING by Reinert, G, Rollin, A

“…Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs. © Applied Probability Trust 2010.…”

Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks by Joanna Raczek

“…We test the proposed algorithm in network models such as trees, geometric random graphs, random graphs and cubic graphs, and we show that the sets of nodes returned by the Minimal_12_Set are in general smaller than sets consisting of nodes chosen randomly.…”
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Limit distributions of maximum vertex degree in a conditional configuration graph by Irina Cheplyukova

“…The degrees of the vertices are independent identically distributed  random variables following the power-law distribution with positive parameter τ. We study the random graphs under the conditions that the sum of vertex degrees does not exceed n and the parameter τ is a random variable uniformly distributed on the interval [a,b], 1≤a<b<∞.  …”
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The Ramsey number of dense graphs by Conlon, D

“…We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree pt and the Ramsey number of random graphs in G(t,p), that is, graphs on t vertices where each edge has been chosen independently with probability p.…”

Poisson approximation of subgraph counts in stochastic block models and a graphon model by Coulson, M, Gaunt, R, Reinert, G

“…Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are isomorphic to some fixed graph. …”

Network Motif Discovery: A GPU Approach by Lin, Wenqing, Xiao, Xiaokui, Xie, Xing, Li, Xiao-Li

“…The basic idea is to employ GPUs to parallelize a large number of subgraph matching tasks in computing subgraph frequencies from random graphs, so as to reduce the overall computation time of network motif discovery. …”
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Lower bounds for adiabatic quantum algorithms by quantum speed limits by Jyong-Hao Chen

“…In particular, we analytically obtain lower bounds on adiabatic algorithms for finding k-clique in random graphs. Additionally, for a particular class of Hamiltonian, it is straightforward to prove the equivalence between our framework and the conventional approach based on spectral gap analysis.…”
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On clustering of conditional configuration graphs by Yury Pavlov

“…We study the subset of such random graphs under the condition that the sum of vertex degrees is known and it is equal to n. …”
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NK-MaxClique and MMCQ: Tow New Exact Branch and Bound Algorithms for the Maximum Clique Problem by Neda Mohammadi, Mehdi Kadivar

“…Simulation results demonstrate that the algorithms outperform the previous well-known algorithms for many instances when applied to DIMACS benchmark and random graphs.…”
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Discrete curvature on graphs from the effective resistance by Devriendt, K, Lambiotte, R

“…Notably, we find a relation to a number of well-established discrete curvatures (Ollivier, Forman, combinatorial curvature) and show evidence for convergence to continuous curvature in the case of Euclidean random graphs. Being both efficient to approximate and highly amenable to theoretical analysis, these resistance curvatures have the potential to shed new light on the theory of discrete curvature and its many applications in mathematics, network science, data science and physics.…”

Entropic barriers as a reason for hardness in both classical and quantum algorithms by Matteo Bellitti, Federico Ricci-Tersenghi, Antonello Scardicchio

“…We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers. …”
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Cluster Persistence for Weighted Graphs by Omer Bobrowski, Primoz Skraba

“…We demonstrate the computational efficiency of our filtration, its practical effectiveness, and explore into its properties when applied to random graphs.…”
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Cycle packing by Conlon, D, Fox, J, Sudakov, B

“…We also prove the Erdős-Gallai conjecture for random graphs and for graphs with linear minimum degree.…”

Graph Imperfection II. by Gerke, S, McDiarmid, C

“…In this paper we show that the imperfection ratio behaves multiplicatively under taking the lexicographic product, which permits us to identify its possible values, investigate its extremal behaviour and its behaviour on random graphs, explore three upper bounds, and show that it is NP-hard to determine. © 2001 Academic Press.…”

On randomly colouring locally sparse graphs by Alan Frieze, Juan Vera

“…For this class of graphs, which includes planar graphs, triangle free graphs and random graphs G {n,p} with p ≪ 1, this beats the 11Δ/6 bound of Vigoda for general graphs.…”
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Resolution of ranking hierarchies in directed networks. by Elisa Letizia, Paolo Barucca, Fabrizio Lillo

“…To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. …”
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