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Number of Connected Components in a Graph: Estimation via Counting Patterns
[article]

2018
*
arXiv
*
pre-print

Inferring

arXiv:1812.00139v1
fatcat:olmz3cwckfc3fh7r2qpgeaib6a
*a*global property*of*the original*graph*from such*a*sampled subgraph is*of**a*fundamental interest.*In*this work, we focus on*estimating*the*number**of**connected**components*. ... This representation is crucial*in*introducing*a*novel*estimator*for the*number**of**connected**components*for general*graphs*, under the knowledge*of*the spectral gap*of*the original*graph*. ... Later entries encode the*count**of*increasingly complex*patterns*: the*number**of*times*a**pattern*is repeated*in*the*graph*. ...##
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Graph Summarization
[article]

2020
*
arXiv
*
pre-print

It denotes

arXiv:2004.14794v3
fatcat:4g4l3exin5dxpoe6pdggbtcory
*a*series*of*application-specific algorithms designed to transform*graphs*into more compact representations while preserving structural*patterns*, query answers, or specific property distributions ... The focus*of*our chapter is to pinpoint the main*graph*summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous ... The target fragment is that*of**counting*regular path queries, which allows one to*estimate*, for example, the*number**of**connections*established*in**a*social network within*a*given period. ...##
###
Graph mining

2006
*
ACM Computing Surveys
*

To answer this, we must first understand what

doi:10.1145/1132952.1132954
fatcat:jbc67scdzbe4vj5o5fjerdy6xq
*patterns*are common*in*real-world*graphs*and can thus be considered*a*mark*of*normality/realism. ... Indeed, any M : N relation*in*database terminology can be represented as*a**graph*.*A*lot*of*these questions boil down to the following: "How can we generate synthetic but realistic*graphs*?" ... Alon et al. [1997] describe*a*deterministic algorithm for*counting*the*number**of*triangles*in**a**graph*. ...##
###
XNN Graph
[chapter]

2016
*
Lecture Notes in Computer Science
*

K-nearest neighbor

doi:10.1007/978-3-319-49055-7_19
fatcat:xeig5btaqfac7iyfwfytfkdnne
*graph*(KNN) is*a*widely used tool*in*several*pattern*recognition applications but it has drawbacks. ... Secondly, KNN does not guarantee*connectivity**of*the*graph*. We introduce an alternative data structure called XNN, which has variable*number**of*neighbors and guarantees*connectivity*. ... The idea generalizes to any*number**of*k by repeating the MST algorithm k. Isolated*component*The main advantage*of*k-MST is that it guarantees*connectivity*. ...##
###
Graph Mining on Streams
[chapter]

2009
*
Encyclopedia of Database Systems
*

Such

doi:10.1007/978-0-387-39940-9_184
fatcat:7lcaeiin7zehvef7ltistncg4m
*a*stream naturally defines an undirected, unweighted*graph**Graph*mining on streams is concerned with*estimating*properties*of*G, or finding*patterns*within G, given the usual constraints*of*the data-stream ... SYNONYMS*Graph*Streams; Semi-Streaming Model DEFINITION Consider*a*data stream*A*=*a*1 ,*a*2 , . . . ,*a*m where each data item*a*k ∈ [n] × [n]. ... Subsequent early work considered*counting*the*number**of*triangles*in**a**graph*[2] and*estimating*common neighborhoods [3] . Again,*a*large*component**of*these results were negative. ...##
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Graph Neural Networks for Graph Drawing
[article]

2022
*
arXiv
*
pre-print

*In*this paper, we propose

*a*novel framework for the development

*of*

*Graph*Neural Drawers (GND), machines that rely on neural computation for constructing efficient and complex maps. ...

*Graph*Drawing techniques have been developed

*in*the last few years with the purpose

*of*producing aesthetically pleasing node-link layouts. ... ACKNOWLEDGMENT The authors would like to thank Giuseppe Di Battista for the insightful discussions and for useful suggestions on the

*Graph*Drawing literature and methods. ...

##
###
Graph Mining on Streams
[chapter]

2016
*
Encyclopedia of Database Systems
*

Subsequent early work considered

doi:10.1007/978-1-4899-7993-3_184-2
fatcat:mcru25yfabh2lj77xhzkw5aoyi
*counting*the*number**of*triangles*in**a**graph*[3] and*estimating*common neighborhoods [4] . Again,*a*large*component**of*these results were negative. ... Such*a*stream naturally defines an undirected, unweighted*graph*G = (V, E) where V = {v 1 , . . . , v n } and ,*Graph*mining on streams is concerned with*estimating*properties*of*G, or finding*patterns*... For*a**graph*with r*connected**components*, it is possible to approximate P 2*in*one pass and O(ǫ −2 m(m − r) −1/4 log δ −1 ) space even if edges may be deleted [14] . ...##
###
Big graph mining

2013
*
SIGKDD Explorations
*

Our findings include anomalous spikes

doi:10.1145/2481244.2481249
fatcat:fzidqzmctndj3nxh2qw55txyuu
*in*the*connected**component*size distribution, the 7 degrees*of*separation*in**a*Web*graph*, and anomalous adult advertisers*in*the who-follows-whom Twitter social network ... How do we find*patterns*and anomalies*in*very large*graphs*with billions*of*nodes and edges? How to mine such big*graphs*efficiently? ... The views and conclusions are those*of*the authors and should not be interpreted as representing the official policies,*of*the U.S. ...##
###
Graph Mining Applications to Social Network Analysis
[chapter]

2010
*
Managing and Mining Graph Data
*

*In*this chapter, we present some

*graph*

*patterns*that are commonly observed

*in*large-scale social networks. ... Network modeling attempts to simulate the real-world network

*via*simple mechanisms such that the

*patterns*presented

*in*large-scale complex networks can be captured. ... =1

*number*

*of*triangles

*connected*to node ∑ =1

*number*

*of*

*connected*triples centered on node = 3 ×

*number*

*of*triangles

*in*the network

*number*

*of*

*connected*triples

*of*nodes (2.6) Figure 16 . 3 . 163

*A*...

##
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DwarvesGraph: A High-Performance Graph Mining System with Pattern Decomposition
[article]

2021
*
arXiv
*
pre-print

*count*

*of*each. ... To

*estimate*implementation cost based on AST, we propose

*a*simple locality-aware and an advanced approximate-mining-based cost model to accurately capture the characteristics

*of*real-world

*graphs*. ... These

*connected*

*components*can merge with VC to produce K sub-

*patterns*. ...

##
###
Graph Transformation Planning via Abstraction

2014
*
Electronic Proceedings in Theoretical Computer Science
*

It features

doi:10.4204/eptcs.159.7
fatcat:nl44jr7bbrcgvkyl35lh5qh3be
*a*domain-independent heuristic that uses the solution length*of*an abstraction*of*the original problem as an*estimate*. ... For the specification*of*reconfigurations, we employ*graph*transformations systems (GTS) due to the close relation*of**graphs*and UML object diagrams. ...*pattern*The target is specified as*a**graph**pattern**in*Figure 3. ...##
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Uncovering Specific-Shape Graph Anomalies in Attributed Graphs

2019
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

The nonlinear approach focuses on optimizing

doi:10.1609/aaai.v33i01.33015433
fatcat:zvksefw4ejgjbkmx4ms6ql3eku
*a*broad class*of*nonlinear cost functions*via*specific-shape constraints*in*attributed*graphs*. ... As networks are ubiquitous*in*the modern era, point anomalies have been changed to*graph*anomalies*in*terms*of*anomaly shapes. ... Acknowledgments This work was supported by the National Key R&D Program*of*China (No. 2018YFC0809800), and partly supported by the NSF grant (No. IIS-1815696). The corresponding author is Wenjun Wang. ...##
###
Random Intersection Graphs and Missing Data

2020
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

We use

doi:10.1609/aaai.v34i04.6010
fatcat:rxzmtbkpancxvbr55kuragpvdq
*graph*properties and theoretical results from random-*graph*theory, such as*connectivity*and the emergence*of*the giant*component*, to identify two threshold phenomena*in*statistical inference with ...*In*this paper we demonstrate the relationship between these two different topics and take*a*novel view*of*the data matrix as*a*random intersection*graph*. ...*A*giant*component*is*a**connected**component**of**a*given random*graph*G = (V, E) that contains*a*finite fraction*of*the entire graph's vertices -O(|V |) (Bollobás 2001). ...##
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Querying in the Age of Graph Databases and Knowledge Graphs
[article]

2021
*
arXiv
*
pre-print

The goal

arXiv:2106.11456v2
fatcat:cuvuubx5pjbmhlh4kmrw43hupi
*of*this document is to provide*a*conceptual map*of*the data management tasks underlying these developments, paying particular attention to data models and query languages for*graphs*. ...*Graphs*have become the best way we know*of*representing knowledge. The computing community has investigated and developed the support for managing*graphs*by means*of*digital technology. ...*A*third tool that is needed then is an efficient algorithm for computing, or*estimating*, the*number**of*solutions to*a*query. ...##
###
The Anatomy of the Facebook Social Graph
[article]

2011
*
arXiv
*
pre-print

First, we characterize the global structure

arXiv:1111.4503v1
fatcat:mfjrldkkhzhhdoja6v3qmh5vem
*of*the*graph*, determining that the social network is nearly fully*connected*, with 99.91%*of*individuals belonging to*a*single large*connected**component*, and ... We compute numerous features*of*the*graph*including the*number**of*users and friendships, the degree distribution, path lengths, clustering, and mixing*patterns*. ... Our neighborhood function calculations only computed distances between pairs*of*users within*connected**components*because these are the only users actually*connected**via*paths. ...
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