Modern Graph Theory

By Béla Bollobás. Graduate Texts in Mathematics, 2002

2,226 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5b2d23a567b117ffe32dad3907a473e328127ff2

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In Computational Theory and Mathematics

Citations in the corpus

Ultrafast consensus in small-world networks (2005, background): “whereν(G) andη(G) are node-connectivity and edge connectivity of a graph, respectively (see [4] for definitions).”
Detecting community structure in networks (2004, neutral): “[44] B.”
Extremal results for random discrete structures (2016, neutral): “, [2], [3], [5], [7]).”
Bounds on graph eigenvalues I (2006, background): “, see [1] and [3]); in particular, we write G (n) for a graph of order n and G (n,m) for a graph of order n and m edges.”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “Here we collect some basic definitions and results on graphs and hypergraphs; see the standard books [15, 31, 32] for further background.”
Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs (2011, background): “Πa := Π ∗ 11 −Π 00Π ∗ 10 −Π ∗ Π∗ 01 −Π∗ 00 0 , (1.10) which is of the form in (1.1). See Remark 5.1 for this reduction. (2) We stress that when n = 1 or N − 1 and the graphs are vertex-transitive [3] (and hence regular) such as tori, the exact locations of mutants become irrelevant. It follows tha”
Evolutionary games on multilayer networks: a colloquium (2015, background): “A single-layer network or a graph is usually given in the form G = ( V, E ) , where V is the set of nodes and E ⊆ V × V corresponds to set of edges that connect said nodes [100].”
Community Structure in Graphs (2007, background): “found in any introductory textbook, like [2].”
Horizontal visibility graphs: exact results for random time series. (2009, background): “Now, for illustration purposes, in figure 7 we show the adjacency matrix [9] of the horizontal visibility graph associated to a random series of 10(3) data (the entry i, j is filled in black if nodes i and j are connected, and left blank otherwise).”
Rigidity and polynomial invariants of convex polytopes (2005, background): “The cyclic order on edges adjacent to the same vertex gives it a structure of a plane graph [Bo].”