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147
Structural Cohesion and Embeddedness: A hierarchical conception of social groups.
 American Sociological Review
, 2000
"... While questions about social cohesion lie at the core of our discipline, definitions are often vague and difficult to operationalize. We link research on social cohesion and social embeddedness by developing a conception of structural cohesion based on network nodeconnectivity. Structural cohesion i ..."
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Cited by 55 (11 self)
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While questions about social cohesion lie at the core of our discipline, definitions are often vague and difficult to operationalize. We link research on social cohesion and social embeddedness by developing a conception of structural cohesion based on network nodeconnectivity. Structural cohesion is defined as the minimum number of actors who, if removed from a group, would disconnect the group. A structural dimension of embeddedness can then be defined through the hierarchical nesting of these cohesive structures. We demonstrate the empirical applicability of our conception of nestedness in two dramatically different substantive settings and discuss additional theoretical implications with reference to a wide array of substantive fields. "...social solidarity is a wholly moral phenomenon which by itself is not amenable to exact observation and especially not to measurement." (Durkheim, (1893 [1984], p.24) "The social structure [of the dyad] rests immediately on the one and on the other of the two, and the secession of either would destroy the whole. ... As soon, however, as there is a sociation of three, a group continues to exist even in case one of the members drops out." (Simmel (1908 [1950], p. 123)
The refined process structure tree
 IBM Research Report RZ
"... Abstract. We consider workflow graphs as a model for the control flow of a business process model and study the problem of workflow graph parsing, i.e., finding the structure of a workflow graph. More precisely, we want to find a decomposition of a workflow graph into a hierarchy of subworkflows th ..."
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Cited by 48 (7 self)
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Abstract. We consider workflow graphs as a model for the control flow of a business process model and study the problem of workflow graph parsing, i.e., finding the structure of a workflow graph. More precisely, we want to find a decomposition of a workflow graph into a hierarchy of subworkflows that are subgraphs with a single entry and a single exit of control. Such a decomposition is the crucial step, for example, to translate a process modeled in a graphbased language such as BPMN into a process modeled in a blockbased language such as BPEL. For this and other applications, it is desirable that the decomposition be unique, modular and as fine as possible, where modular means that a local change of the workflow graph can only cause a local change of the decomposition. In this paper, we provide a decomposition that is unique, modular and finer than in previous work. It is based on and extends similar work for sequential programs by Tarjan and Valdes [11]. We show that our decomposition can be computed in linear time based on an algorithm by Hopcroft and Tarjan [3] that finds the triconnected components of a biconnected graph.
Social Cohesion and Embeddedness: A hierarchical conception of social groups
, 2002
"... While questions about social cohesion lie at the core of our discipline, no clear definition of cohesion exists. We present a definition of social cohesion based on network connectivity that leads to an operationalization of social embeddedness. We define cohesiveness as the minimum number of actors ..."
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Cited by 35 (19 self)
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While questions about social cohesion lie at the core of our discipline, no clear definition of cohesion exists. We present a definition of social cohesion based on network connectivity that leads to an operationalization of social embeddedness. We define cohesiveness as the minimum number of actors who, if removed from a group, would disconnect the group. This definition generates hierarchically nested groups, where highly cohesive groups are embedded within less cohesive groups. We discuss the theoretical implications of this definition and demonstrate the empirical applicability of our conception of nestedness by testing the predicted correlates of our cohesion measure within high school friendship and interlocking directorate networks. Keywords: Social networks, social theory, social cohesion, connectivity algorithm, embeddedness. "...social solidarity is a wholly moral phenomenon which by itself is not amenable to exact observation and especially not to measurement." (Durkheim, (1893 [1984], p.24) "The social structure [of the dyad] rests immediately on the one and on the other of the two, and the secession of either would destroy the whole. ... As soon, however, as there is a sociation of three, a group continues to exist even in case one of the members drops out." (Simmel (1908 [1950], p. 123)
Algorithms for Square Roots of Graphs
 SIAM Journal on Discrete Mathematics
, 1991
"... The nth power (n 1) of a graph G = (V; E), written G n , is defined to be the graph having V as its vertex set with two vertices u; v adjacent in G n if and only if there exists a path of length at most n between them. Similarly, graph H has an nth root G if G n = H . For the case of n = 2, ..."
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Cited by 34 (0 self)
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The nth power (n 1) of a graph G = (V; E), written G n , is defined to be the graph having V as its vertex set with two vertices u; v adjacent in G n if and only if there exists a path of length at most n between them. Similarly, graph H has an nth root G if G n = H . For the case of n = 2, we say that G 2 is the square of G and G is the square root of G 2 . Here we give a linear time algorithm for finding the tree square roots of a given graph and a linear time algorithm for finding the square roots of planar graphs. We also give a polynomial time algorithm for finding the square roots of subdivision graphs, which is equivalent to the problem of the inversion of total graphs. Further, we give a linear time algorithm for finding a Hamiltonian cycle in a cubic graph, and we prove the NPcompleteness of finding the maximum cliques in powers of graphs and the chordality of powers of trees. Keywords: Square graphs, power graphs, tree square, planar square graphs. 1 Introduct...
Optimal upward planarity testing of singlesource digraphs
 SIAM Journal on Computing
, 1998
"... Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in softwar ..."
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Cited by 34 (4 self)
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Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of singlesource digraphs; we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a singlesource digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with n log log n / log n processors, using O(n) space. The algorithm also constructs an upward planar drawing if the test is successful. The previously known best result is an O(n2)time algorithm by Hutton and Lubiw [Proc. 2nd ACM–SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1991, pp. 203–211]. No efficient parallel algorithms for upward planarity testing were previously known.
Pathbased depthfirst search for strong and biconnected components
 Information Processing Letters
, 2000
"... Key words: Graph, depthfirst search, strongly connected component, biconnected component, stack. ..."
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Cited by 30 (0 self)
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Key words: Graph, depthfirst search, strongly connected component, biconnected component, stack.
Finding Triconnected Components By Local Replacement
, 1993
"... . We present a parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(log n) and the processortime product is O((m + n) log log n) where n is the number of vertices, and m is the number of edges of the input graph. Our algorithm, like other ..."
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Cited by 29 (6 self)
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. We present a parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(log n) and the processortime product is O((m + n) log log n) where n is the number of vertices, and m is the number of edges of the input graph. Our algorithm, like other parallel algorithms for this problem, is based on open ear decomposition but it employs a new technique, local replacement, to improve the complexity. Only the need to use the subroutines for connected components and integer sorting, for which no optimal parallel algorithm that runs in O(log n) time is known, prevents our algorithm from achieving optimality. 1. Introduction. A connected graph G = (V; E) is kvertex connected if it has at least (k + 1) vertices and removal of any (k \Gamma 1) vertices leaves the graph connected. Designing efficient algorithms for determining the connectivity of graphs has been a subject of great interest in the last two decades. Applications of graph connect...
Improved Sparsification
, 1993
"... In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using ..."
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Cited by 28 (5 self)
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In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using our improved sparsification technique, we keep track of the following properties: minimum spanning forest, best swap, connectivity, 2edgeconnectivity, and bipartiteness, in time O(n 1/2 ) per edge insertion or deletion; 2vertexconnectivity and 3vertexconnectivity, in time O(n) per update; and 4vertexconnectivity, in time O(n#(n)) per update.
ONLINE PLANARITY TESTING
, 1996
"... The online planaritytesting problem consists of performing the following operations on a planar graph G: (i) testing if a new edge can be added to G so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for online plan ..."
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Cited by 26 (2 self)
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The online planaritytesting problem consists of performing the following operations on a planar graph G: (i) testing if a new edge can be added to G so that the resulting graph is itself planar; (ii) adding vertices and edges such that planarity is preserved. An efficient technique for online planarity testing of a graph is presented that uses O(n) space and supports tests and insertions of vertices and edges in O(log n) time, where n is the current number of vertices of G. The bounds for tests and vertex insertions are worstcase and the bound for edge insertions is amortized. We also present other applications of this technique to dynamic algorithms for planar graphs.
A new graph triconnectivity algorithm and its parallelization
 Combinatorica
, 1987
"... We present a new algorithm for finding the triconnected components of an undirected graph. The algorithm is based on a method of searching graphs called ‘open ear decomposition’. A parallel implementation of the algorithm on a CRCW PRAM runs in O(log 2 n) parallel time using O(n + m) processors, whe ..."
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Cited by 25 (3 self)
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We present a new algorithm for finding the triconnected components of an undirected graph. The algorithm is based on a method of searching graphs called ‘open ear decomposition’. A parallel implementation of the algorithm on a CRCW PRAM runs in O(log 2 n) parallel time using O(n + m) processors, where n is the number of vertices and m is the number of edges in the graph.