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213,911
Graph topologies on closed multifunctions
, 2003
"... In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X × Y using various h-pertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X × Y. We also study several topologies ..."
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In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X × Y using various h-pertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X × Y. We also study several
Network Robustness and Graph Topology
, 2004
"... Two important recent trends in military and civilian communications have been the increasing tendency to base operations around an internal network, and the increasing threats to communications infrastructure. This combination of factors makes it important to study the robustness of network topologi ..."
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Cited by 37 (5 self)
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topologies. We use graph-theoretic concepts of connectivity to do this, and argue that node connectivity is the most useful such measure. We examine the relationship between node connectivity and network symmetry, and describe two conditions which robust networks should satisfy. To assist with the process
THE CARRIER GRAPH TOPOLOGY
"... Abstract. We define a new metric on the set of all closed linear operators between Hilbert spaces and investigate its properties. In particular, we show that the set of all closed operators with a closed range is an open subset of the set of all closed operators and the map T 7 → T † is an isometry ..."
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in this metric. We also investigate the relationships between the topology induced by this metric and the gap metric. 1.
GRAPHS, TOPOLOGIES AND SIMPLE GAMES
, 2000
"... We study the existence of connected coalitions in a simple game restricted by a partial order. First, we define a topology compatible with the partial order in the set of players. Second, we prove some properties of the covering and comparability graphs of a finite poset. Finally, we analize the cor ..."
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We study the existence of connected coalitions in a simple game restricted by a partial order. First, we define a topology compatible with the partial order in the set of players. Second, we prove some properties of the covering and comparability graphs of a finite poset. Finally, we analize
Exploiting Graph Topology For Optimization Problems
, 1996
"... . Constraint 1 satisfaction problems can be modeled as graphs with the decision points represented as vertices and constraints drawn as edges. Graphs can be one-dimensional (trees), two-dimensional (planes), three-dimensional (cubes), etc., up to N-dimensional (cliques), or combinations of any of ..."
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can have their complexity significantly reduced. In this paper, we present the key concepts and algorithms behind this approach and apply the results to graph coloring and natural language semantic analysis. We also introduce a new measure of complexity, discuss its relationship to graph topology
Pregel: A system for large-scale graph processing
- IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
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Cited by 492 (0 self)
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model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach
Modeling Internet Topology
- IEEE COMMUNICATIONS MAGAZINE
, 1997
"... The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph-based ..."
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Cited by 493 (21 self)
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The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph
Distinguishing Infections on Different Graph Topologies
, 2014
"... The history of infections and epidemics holds famous examples where understand-ing, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to person, device to device, through contact networks; Cholera, Canc ..."
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, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the grid, and the Erdös-Renyi graphs. 1
On Power-Law Relationships of the Internet Topology
- IN SIGCOMM
, 1999
"... Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period. We show that our power-l ..."
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Cited by 1668 (71 self)
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Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period. We show that our power
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213,911
