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The SmallWorld Phenomenon: An Algorithmic Perspective
 in Proceedings of the 32nd ACM Symposium on Theory of Computing
, 2000
"... Long a matter of folklore, the “smallworld phenomenon ” — the principle that we are all linked by short chains of acquaintances — was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960’s. This work was among the first to m ..."
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Cited by 824 (5 self)
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Long a matter of folklore, the “smallworld phenomenon ” — the principle that we are all linked by short chains of acquaintances — was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960’s. This work was among the first
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 507 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
Small degree outbranchings
, 2001
"... Using a suitable orientation, we give a short proof of a result of Czumaj and Strothmann [3]: Every 2edgeconnected graph G contains a spanning tree T with the property that dT (v) ≤ dG(v)+3 for every vertex v. 2 Trying to find an analogue of this result in the directed case, we prove that every 2 ..."
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Cited by 3 (0 self)
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Using a suitable orientation, we give a short proof of a result of Czumaj and Strothmann [3]: Every 2edgeconnected graph G contains a spanning tree T with the property that dT (v) ≤ dG(v)+3 for every vertex v. 2 Trying to find an analogue of this result in the directed case, we prove that every 2arcstrong digraph D has an outbranching B such that d + d+
DIOPHANTINE APPROXIMATION IN SMALL DEGREE
, 2003
"... This paper (partly a survey) deals with the problem of finding optimal exponents in Diophantine estimates involving one real number ξ. The prototype of such an estimate is the fact, known at least since Euler, that, for any given irrational real number ξ, there exist ..."
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Cited by 2 (0 self)
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This paper (partly a survey) deals with the problem of finding optimal exponents in Diophantine estimates involving one real number ξ. The prototype of such an estimate is the fact, known at least since Euler, that, for any given irrational real number ξ, there exist
Spanning trees of small degree by
"... Abstract. In this paper we show that pseudorandom graphs contain spanning trees of maximum degree 3. More specifically, (n, d, λ)graphs with sufficiently large spectral gap contain such spanning trees. 1. ..."
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Abstract. In this paper we show that pseudorandom graphs contain spanning trees of maximum degree 3. More specifically, (n, d, λ)graphs with sufficiently large spectral gap contain such spanning trees. 1.
Finding small degree factors of . . .
, 2006
"... We present algorithms that compute all irreducible factors of degree â¤ d of supersparse (lacunary) multivariate polynomials in n variables over an algebraic number field in deterministic polynomialtime in (l+d) n, where l is the size of the input polynomial. In supersparse polynomials, the term d ..."
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We present algorithms that compute all irreducible factors of degree â¤ d of supersparse (lacunary) multivariate polynomials in n variables over an algebraic number field in deterministic polynomialtime in (l+d) n, where l is the size of the input polynomial. In supersparse polynomials, the term
ON MANIFOLDS OF SMALL DEGREE
, 2003
"... ABSTRACT. Let X ⊂ P n be a complex projective manifold of degree d and arbitrary dimension. The main result of this paper gives a classification of such manifolds (assumed moreover to be connected, nondegenerate and linearly normal) in case d � n. As a byproduct of the classification it follows th ..."
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ABSTRACT. Let X ⊂ P n be a complex projective manifold of degree d and arbitrary dimension. The main result of this paper gives a classification of such manifolds (assumed moreover to be connected, nondegenerate and linearly normal) in case d � n. As a byproduct of the classification it follows
Fault Tolerant Networks With Small Degree
 In Proceedings of the 12th ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2000
"... In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G # is called a kfaulttolerant graph of G if when we remove any k nodes from G # , it still contains a subg ..."
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Cited by 15 (0 self)
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tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree O(1) for arrays and O(log 3 k) for meshes. The number of spare nodes used are O(k log 2 k) and O(k 2 / log k), respectively. Compared to the previous results, the number of spare nodes used in our
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 2600 (7 self)
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, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Centrality in social networks conceptual clarification
 Social Networks
, 1978
"... The intuitive background for measures of structural centrality in social networks is reviewed aPzd existing measures are evaluated in terms of their consistency with intuitions and their interpretability. Three distinct intuitive conceptions of centrality are uncovered and existing measures are refi ..."
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Cited by 1083 (2 self)
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are refined to embody these conceptions. Three measures are developed for each concept, one absolute and one relative measure of the ~entra~~t~ ~ of ~os~tio~ls in a network, and one relenting the degree of centralization of the entire network. The implications of these measures for the experimental study
Results 1  10
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13,343