Network structure and minimum degree

By S. Seidman. 1983

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Citations in the corpus

Text Categorization as a Graph Classification Problem (2015, background): “Seidman (1983) deﬁned the k -core of a graph as the maximal connected subgraph whose vertices are at least of degree k within the subgraph.”
Community detection in graphs (2009, background): “The most popular quality function is the modularity of Newman and Girvan (Newman and Girvan, 2004).”
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem (2011, methodology): “Degree based models of cohesion, which overcome the drawbacks inherent in the definitions of k-clique and k-club, were first introduced in [Seidman and Foster, 1978] and [Seidman, 1983].”
Structure and dynamics of core/periphery networks (2013, background): “k-core a maximal connected subgraph, where the elements of the subgraph are connected to at least k other elements of the same subgraph; alternatively: the union of all k-shells with indices greater or equal k, where the k-shell is defined as the set of consecutively removed nodes and belonging link”
An O(m) Algorithm for Cores Decomposition of Networks (2003, background): “cally diﬃcult (NP hard [4] or at least quadratic), but for cores a very eﬃcient algorithm exists. We describe it in details in this paper. 2 Cores The notion of core was introduced by Seidman in 1983 [6]. Let G = (V,L) be a graph. V is the set of vertices and L is the set of lines (edges or arcs). W”
The n-ordered graphs: A new graph class (2009, background): “If an n-core H of G is nontrivial, then ‐(H) ‚ n+1: For more on n-cores, see [1, 11 ].”
Main Core Retention on Graph-of-Words for Single-Document Keyword Extraction (2015, methodology): “The idea of a k-degenerate graph comes from the work of Bollobás in [5, page 222] that was further extended by Seidman in [23] into the notion of a k-core, which explains the use of degeneracy as an alternative denomination in the literature.”
Information diffusion in online social networks: a survey (2013, methodology): “identified by the k-core decomposition analysis [45], as defined in Definition 9.”
Visualizing Bibliometric Networks (2014, background): “The identification of core publications is based on the idea of k-cores introduced by Seidman (1983).”
ASK-GraphView: A Large Scale Graph Visualization System (2006, methodology): “We use a special case of a linear time process known as peeling [3,9,21] to identify peripheral tree-like sections and group them together.”
Assessing the bias in samples of large online networks (2014, methodology): “he plots consider two measures of user centrality, degree and kore (Bonacich, 1987; Seidman, 1983); they were calculated using he networks aggregated for the full observation period.”
Identifying influential spreaders in complex networks (2010, unknown): “Instead, we find that the most efficient spreaders are those located within the core of the network as identified by the k -shell decomposition analysi”
Identifying sets of key players in a social network (2006, background): “In addition, work on identifying cores and peripheries (e.g., Seidman, 1983; Borgatti and Everett, 1999; Everett and Borgatti, 1999a) is relevant, as is work on group-level centrality (Everett and Borgatti, 1999b).”