Emergence of Scaling in Random Networks

By B. McInnes, Jannene S. McBride, N. Evans, David D. Lambert, A. Andrew. 1999

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In Scaling & Learning Theory

Citations in the corpus

Neural Execution Engines: Learning to Execute Subroutines (2020, background): “In Figure 9, we show the strong generalization performance of the different architectures.”
Gradient-Based Neural DAG Learning (2019, methodology): “Scale-free (SF) graphs were generated using the Barab´asi-Albert model (Barab´asi & Albert, 1999) which is based on preferential attachment.”
Attacking Graph-based Classification via Manipulating the Graph Structure (2019, background): “, Preferential Attachment [4]) developed by the network science community to synthesize the positive nodes and edges.”
Graphite: Iterative Generative Modeling of Graphs (2018, methodology): “…since; for e.g. , the small-world graphs model generates graphs with small diameter and hence the generated graphs exhibit strong local clustering [51], the Barabasi-Albert models preferential attachment whereby nodes high-degree nodes are likely to form edges with newly added nodes [1] etc.”
GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders (2018, background): “Related work pre-dating deep learning includes random graphs (Erdos & R´enyi, 1960; Barab´asi & Albert, 1999), stochastic blockmodels (Snijders & Nowicki, 1997), or state transition matrix learning (Gong & Xiang, 2003).”
Learning Deep Generative Models of Graphs (2018, methodology): “One approach, based on random graph models, robustly assign probabilities to large classes of graphs (Erd ˝ os & Rényi, 1960; Barabási & Albert, 1999).”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, methodology): “Since real-world networks often exhibit scale-free and small-world topologies (Watts and Strogatz, 1998; Barab´asi and Albert, 1999) with highly connected hub nodes, these kinds of structural assumptions are not only diﬃcult to satisfy, but impossible to check.”
Community detection in graphs (2009, methodology): “Due to the important implications that broad degree distributions have for the structure and function of real networks (Albert and Barabási, 2002; Barrat et al., 2008; Boccaletti et al., 2006; Dorogovtsev and Mendes, 2002; Newman, 2003; Pastor-Satorras and Vespignani, 2004), it is preferable to go ”
A Review of Relational Machine Learning for Knowledge Graphs (2015, background): “Local similarity indices such as Common Neighbors , the Adamic-Adar index [94] or Preferential Attachment [95] derive the similarity of entities from their number of common neighbors or their absolute number of neighbors.”
Supervised random walks: predicting and recommending links in social networks (2010, background): “Moreover, even models of complex networks, like Preferential Attachment [7], Forest Fire model [20] and models based on random walks [19, 8], can be viewed as ways for predicting new links in networks.”
The Diameter of Random Sparse Graphs (2000, methodology): “Nevertheless, many of the methods and ideas [1, 2, 3, 5, 7] that are used in modeling and analyzing massive graphs have been frequently traced to the seminal papers of Erdős and Rényi [13] in 1959.”
Watching television over an IP network (2008, background): “The graph after the 4-second mark follows a power-law distribution [23,24].”
Simple models of human brain functional networks (2012, background): “Growth models for the formation of other real-life complex systems have previously been more successful by including an additional topological term in the connection probability function (19, 22), for example:”