Results 1  10
of
16
Expansion and lack thereof in randomly perturbed graphs
 Internet Math
"... Developing models of complex networks has been a major industry in the fields of physics, mathematics, and computer science during the last decade. Empirical study of numerous large networks harvested from the real world has revealed that, unlike the classical models of random graphs developed ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
(Show Context)
Developing models of complex networks has been a major industry in the fields of physics, mathematics, and computer science during the last decade. Empirical study of numerous large networks harvested from the real world has revealed that, unlike the classical models of random graphs developed
Small Worlds as Navigable Augmented Networks — Model, Analysis, and Validation —
"... Abstract. The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closel ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closely related individuals, based solely on some characteristics of the target (professional occupation, state of leaving, etc.). In his paper on small world navigability, Jon Kleinberg modeled this phenomenon in the framework of augmented networks, and analyzed the performances of greedy routing in augmented multidimensional meshes. This paper objective is to survey the results that followed up Kleinberg seminal work, including results about: – extensions of the augmented network model, and variants of greedy routing, – designs of polylognavigable graph classes, – the quest for universal augmentation schemes, and
Drawing power law graphs
 IN PROCEEDINGS OF INTERNATIONAL SYMPOSIUM ON GRAPH DRAWING (GD2004)
, 2004
"... We present methods for drawing graphs that arise in various information networks. It has been noted that many realistic graphs have power law degree distribution and exhibit the small world phenomenon. Our algorithm is influenced by recent developments on modeling and analysis of such power law grap ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We present methods for drawing graphs that arise in various information networks. It has been noted that many realistic graphs have power law degree distribution and exhibit the small world phenomenon. Our algorithm is influenced by recent developments on modeling and analysis of such power law graphs.
Faster random walks by rewiring online social networks onthefly
 In ICDE
, 2013
"... Abstract — Many online social networks feature restrictive web interfaces which only allow the query of a user’s local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chai ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
Abstract — Many online social networks feature restrictive web interfaces which only allow the query of a user’s local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chain Monte Carlo methods such as random walks to sample the social network and support analytics based on the samples. The problem with such an approach, however, is the large amount of queries often required (i.e., a long “mixing time”) for a random walk to reach a desired (stationary) sampling distribution. In this paper, we consider a novel problem of enabling a faster random walk over online social networks by “rewiring ” the social network onthefly. Specifically, we develop Modified TOpology (MTO)Sampler which, by using only information exposed by the restrictive web interface, constructs a “virtual ” overlay topology of the social network while performing a random walk, and ensures that the random walk follows the modified overlay topology rather than the original one. We show that MTOSampler not only provably enhances the efficiency of sampling, but also achieves significant savings on query cost over realworld online social networks such as Google Plus, Epinion etc. I.
Modeling the smallworld phenomenon with local network flow
"... The smallworld phenomenon includes both small average distance and the clustering effect. Randomly generated graphs with a power law degree distribution are widely used to model large realworld networks, but while these graphs have small average distance, they generally do not exhibit the clusteri ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
The smallworld phenomenon includes both small average distance and the clustering effect. Randomly generated graphs with a power law degree distribution are widely used to model large realworld networks, but while these graphs have small average distance, they generally do not exhibit the clustering effect. We introduce an improved hybrid model which combines a global graph (a random power law graph) with a local graph (a graph with high local connectivity defined by network flow). We present an efficient algorithm which extracts a local graph from a given realistic network. We show that the underlying local graph is robust in the sense that when our extraction algorithm is applied to a hybrid graph, it recovers the original local graph with a small error. The proof involves a probabilistic analysis of the growth of neighborhoods in the hybrid graph model.
Exchangeable random networks
 Internet Mathematics
"... We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that characterize the degree distribution of the ensemble graphs, together with some fe ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that characterize the degree distribution of the ensemble graphs, together with some features that are important for applications, such as subgraph distributions and kernel of the adjacency matrix. A particular case of directed networks with powerlaw out–degree is studied in more detail, as an example of the flexibility of the model in applications. Key words and phrases
Recovering the long range links in Augmented graphs
 n o RR6197, Institut National de Recherche en Informatique et Automatique (INRIA), 2007, https:// hal.inria.fr/inria00147536. References in notes
"... Abstract. The augmented graph model, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair (H, ϕ), where H is a graph in which internode distances are supposed to be easy to compute or at least easy t ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. The augmented graph model, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair (H, ϕ), where H is a graph in which internode distances are supposed to be easy to compute or at least easy to estimate. This graph is ”augmented ” by links, called longrange links, which are selected according to the probability distribution ϕ. The augmented graph model enables the analysis of greedy routing in augmented graphs G ∈ (H, ϕ). In greedy routing, each intermediate node handling a message for a target t selects among all its neighbors in G the one that is the closest to t in H and forwards the message to it. This paper addresses the problem of checking whether a given graph G is an augmented graph. It answers part of the questions raised by Kleinberg in his Problem 9 (Int. Congress of Math. 2006). More precisely, given G ∈ (H, ϕ), we aim at extracting the base graph H and
Chinese Academy of Sciences
, 2004
"... Abstract There have been several algorithms for mining association rules, such as Apriori and some improved Aprioris, only to be Interested in those itemsets, which have support above a userdefined threshold. However, there exists a kind of important rule, indirect association, hidden in these item ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract There have been several algorithms for mining association rules, such as Apriori and some improved Aprioris, only to be Interested in those itemsets, which have support above a userdefined threshold. However, there exists a kind of important rule, indirect association, hidden in these itemsets, which are filtered. out. When a pair of items, (A, B), which seldom. occur together in the same transaction, are highly dependent on the presence of another itemset, Z, the pair (A, B) are said to be indirectly associated via Z In this paper, the definition of indirect association is firstly given. Then a measure of dependence to estimate the correlation between relative frequent items and a simple way to express the closeness between a pair of items indirectly associated by another itemset are provided. In addition, two kinds of classifying standard for indirect association rules are proposed for further research. In order to mine such indirect association rules, an algorithm of indirect association mining (IAM) is presented. And the complexity analysis about this algorithm is showed. An experiment in order to verify the utility of this algorithm is made. Finally, some issues about the IAM algorithm are put forward for future research. Krywords data mining, ossociafion rule, indirect associalion, the bridge itemset. IAM I.