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

Ashish Khetan, Harshay Shah, Sewoong Oh
2018 arXiv   pre-print
Inferring 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.  ... 
arXiv:1812.00139v1 fatcat:olmz3cwckfc3fh7r2qpgeaib6a

Graph Summarization [article]

Angela Bonifati, Stefania Dumbrava, Haridimos Kondylakis
2020 arXiv   pre-print
It denotes 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.  ... 
arXiv:2004.14794v3 fatcat:4g4l3exin5dxpoe6pdggbtcory

Graph mining

Deepayan Chakrabarti, Christos Faloutsos
2006 ACM Computing Surveys  
To answer this, we must first understand what 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.  ... 
doi:10.1145/1132952.1132954 fatcat:jbc67scdzbe4vj5o5fjerdy6xq

XNN Graph [chapter]

Pasi Fränti, Radu Mariescu-Istodor, Caiming Zhong
2016 Lecture Notes in Computer Science  
K-nearest neighbor 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.  ... 
doi:10.1007/978-3-319-49055-7_19 fatcat:xeig5btaqfac7iyfwfytfkdnne

Graph Mining on Streams [chapter]

Linda L. Hill, Mehmet M. Dalkiliç, Brahim Medjahed, Mourad Ouzzani, Ahmed K. Elmagarmid, Joseph M. Hellerstein, Colin R. Reeves, Christopher B. Jones, Ross S. Purves, Michael F. Goodchild, Jayant Sharma, John Herring (+24 others)
2009 Encyclopedia of Database Systems  
Such 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.  ... 
doi:10.1007/978-0-387-39940-9_184 fatcat:7lcaeiin7zehvef7ltistncg4m

Graph Neural Networks for Graph Drawing [article]

Matteo Tiezzi, Gabriele Ciravegna, Marco Gori
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.  ... 
arXiv:2109.10061v2 fatcat:lu4he24ppbd3lj2wtrz46tdbma

Graph Mining on Streams [chapter]

Andrew McGregor
2016 Encyclopedia of Database Systems  
Subsequent early work considered 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] .  ... 
doi:10.1007/978-1-4899-7993-3_184-2 fatcat:mcru25yfabh2lj77xhzkw5aoyi

Big graph mining

U. Kang, Christos Faloutsos
2013 SIGKDD Explorations  
Our findings include anomalous spikes 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.  ... 
doi:10.1145/2481244.2481249 fatcat:fzidqzmctndj3nxh2qw55txyuu

Graph Mining Applications to Social Network Analysis [chapter]

Lei Tang, Huan Liu
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  ... 
doi:10.1007/978-1-4419-6045-0_16 dblp:series/ads/TangL10 fatcat:ydikf7xblvah5a36nazj6idwje

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

Jingji Chen, Xuehai Qian
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.  ... 
arXiv:2008.09682v3 fatcat:owamj4cn7jbhjkr4zorxiebon4

Graph Transformation Planning via Abstraction

Steffen Ziegert
2014 Electronic Proceedings in Theoretical Computer Science  
It features 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.  ... 
doi:10.4204/eptcs.159.7 fatcat:nl44jr7bbrcgvkyl35lh5qh3be

Uncovering Specific-Shape Graph Anomalies in Attributed Graphs

Nannan Wu, Wenjun Wang, Feng Chen, Jianxin Li, Bo Li, Jinpeng Huai
The nonlinear approach focuses on optimizing 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.  ... 
doi:10.1609/aaai.v33i01.33015433 fatcat:zvksefw4ejgjbkmx4ms6ql3eku

Random Intersection Graphs and Missing Data

Dror Salti, Yakir Berchenko
We use 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).  ... 
doi:10.1609/aaai.v34i04.6010 fatcat:rxzmtbkpancxvbr55kuragpvdq

Querying in the Age of Graph Databases and Knowledge Graphs [article]

Marcelo Arenas and Claudio Gutierrez and Juan F. Sequeda
2021 arXiv   pre-print
The goal 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.  ... 
arXiv:2106.11456v2 fatcat:cuvuubx5pjbmhlh4kmrw43hupi

The Anatomy of the Facebook Social Graph [article]

Johan Ugander, Brian Karrer, Lars Backstrom, Cameron Marlow
2011 arXiv   pre-print
First, we characterize the global structure 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.  ... 
arXiv:1111.4503v1 fatcat:mfjrldkkhzhhdoja6v3qmh5vem
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