Complex Graphs and Networks

By Fan Chung, Linyuan Lu. 2006

833 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8fc012941dccba5017bfd73dfd40e414001b74c4

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In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel (2013, methodology): “Applying Lemma B.1, we have For the second term, ﬁrst we apply the two sided concentration inequality for each i , (see for example Chung and Lu [18, chap.”
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem (2011, background): “Our interest in such graphs stems from the ubiquitous presence of power law degree distribution [Chung and Lu, 2006] in natural and man-made networks including social and biological networks, well documented in the past decade [Barabási and Albert, 1999, Barabási et al.”
Distributed Consensus Algorithms in Sensor Networks With Imperfect Communication: Link Failures and Channel Noise (2007, methodology): “we consider a network of N = 100 nodes withM = 5N edges (generated according to an Erdös-Renýi graph, see [37].”
A Survey of Statistical Network Models (2009, background): “Chung and Lu [69] provide a complementary treatment of these models and their probabilistic properties.”
A survey of random processes with reinforcement (2006, background): “ghly the derivative with respect to −d of k(d), namely 2m2n/d3. Thus the fraction of vertices having degree exactly d should be asymptotic to 2m2/d3. Chapter 3 of the forthcoming book of Chung and Lu [CL06a] will contain the ﬁrst rigorous and somewhat comprehensive treatment of preferential attachme”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, methodology): “hose number of zero eigenvalues is equivalent to the number of components of the graph. Spectral properties of the graph Laplacian can also be related to expansion, diameter, distance between subsets [24,25]. 2.2. Simplicial Complexes. Consider a nite set of vertices V. A k-simplex S kis a subset of”
Protecting privacy when mining and sharing user data (2012, background): “More specifically, let n be the total number of nodes in G, ↵ (2 < ↵  3, [35]) be the power law parameter; and d”
Concentration Inequalities and Martingale Inequalities: A Survey (2006, background): “The details of the proof can be found in a forthcoming book [Chung and Lu 06].”
A nonparametric view of network models and Newman–Girvan and other modularities (2009, methodology): “(2) from a statistical point of view and in Chung and Lu (8) for a probabilistic one.”
Growth of preferential attachment random graphs via continuous-time branching processes (2007, background): “Recently, Barabasi and Albert [7] proposed a random graph version of these processes as a model for several realworld networks, such as the internet and various communication structures, on which there has been much renewed study (see [1], [9], [11], [15] and references therein).”
Analyzing and modeling real-world phenomena with complex networks: a survey of applications (2007, background): “[8,9], after which the theory of graphs has been useful for theoretical physics, economy, sociology and biology.”
First passage percolation on random graphs with finite mean degrees (2009, neutral): “For introductions to scale-free random graphs, we refer to the monographs [12, 17], for surveys of classical random graphs focussing on the Erdős–Rényi random graph (see [8, 25]).”
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters (2008, methodology): “) Given the number of nodes n, the power-law exponent β, and the parameters w and wmax, [Chung and Lu 06a] gives the degree sequence for a power-law graph:”
Kronecker Graphs: An Approach to Modeling Networks (2008, background): “This suggests a network structure which is also known ascore-periphery(Borgatti and Everett, 2000; Holme, 2005), thej llyfish(Tauro et al., 2001; Siganos et al., 2006), or theoctopus(Chung and Lu, 2006) structure of the network as illustrated in Figure 24(c).”