%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/DIMACS10/road_central
% name: DIMACS10/road_central
% [DIMACS10 set: clustering/road_central]
% id: 2458
% date: 2011
% author: unknown
% ed: H. Meyerhenke
% fields: name title A id date author ed kind notes
% kind: undirected graph
%-------------------------------------------------------------------------------
% notes:
% 10th DIMACS Implementation Challenge:                                   
%                                                                         
% http://www.cc.gatech.edu/dimacs10/index.shtml                           
%                                                                         
% As stated on their main website (                                       
% http://dimacs.rutgers.edu/Challenges/ ), the "DIMACS Implementation     
% Challenges address questions of determining realistic algorithm         
% performance where worst case analysis is overly pessimistic and         
% probabilistic models are too unrealistic: experimentation can provide   
% guides to realistic algorithm performance where analysis fails."        
%                                                                         
% For the 10th DIMACS Implementation Challenge, the two related           
% problems of graph partitioning and graph clustering were chosen.        
% Graph partitioning and graph clustering are among the aforementioned    
% questions or problem areas where theoretical and practical results      
% deviate significantly from each other, so that experimental outcomes    
% are of particular interest.                                             
%                                                                         
% Problem Motivation                                                      
%                                                                         
% Graph partitioning and graph clustering are ubiquitous subtasks in      
% many application areas. Generally speaking, both techniques aim at      
% the identification of vertex subsets with many internal and few         
% external edges. To name only a few, problems addressed by graph         
% partitioning and graph clustering algorithms are:                       
%                                                                         
%     * What are the communities within an (online) social network?       
%     * How do I speed up a numerical simulation by mapping it            
%         efficiently onto a parallel computer?                           
%     * How must components be organized on a computer chip such that     
%         they can communicate efficiently with each other?               
%     * What are the segments of a digital image?                         
%     * Which functions are certain genes (most likely) responsible       
%         for?                                                            
%                                                                         
% Challenge Goals                                                         
%                                                                         
%     * One goal of this Challenge is to create a reproducible picture    
%         of the state-of-the-art in the area of graph partitioning       
%         (GP) and graph clustering (GC) algorithms. To this end we       
%         are identifying a standard set of benchmark instances and       
%         generators.                                                     
%                                                                         
%     * Moreover, after initiating a discussion with the community, we    
%         would like to establish the most appropriate problem            
%         formulations and objective functions for a variety of           
%         applications.                                                   
%                                                                         
%     * Another goal is to enable current researchers to compare their    
%         codes with each other, in hopes of identifying the most         
%         effective algorithmic innovations that have been proposed.      
%                                                                         
%     * The final goal is to publish proceedings containing results       
%         presented at the Challenge workshop, and a book containing      
%         the best of the proceedings papers.                             
%                                                                         
% Problems Addressed                                                      
%                                                                         
% The precise problem formulations need to be established in the course   
% of the Challenge. The descriptions below serve as a starting point.     
%                                                                         
%     * Graph partitioning:                                               
%                                                                         
%       The most common formulation of the graph partitioning problem     
%       for an undirected graph G = (V,E) asks for a division of V into   
%       k pairwise disjoint subsets (partitions) such that all            
%       partitions are of approximately equal size and the edge-cut,      
%       i.e., the total number of edges having their incident nodes in    
%       different subdomains, is minimized. The problem is known to be    
%       NP-hard.                                                          
%                                                                         
%     * Graph clustering:                                                 
%                                                                         
%       Clustering is an important tool for investigating the             
%       structural properties of data. Generally speaking, clustering     
%       refers to the grouping of objects such that objects in the same   
%       cluster are more similar to each other than to objects of         
%       different clusters. The similarity measure depends on the         
%       underlying application. Clustering graphs usually refers to the   
%       identification of vertex subsets (clusters) that have             
%       significantly more internal edges (to vertices of the same        
%       cluster) than external ones (to vertices of another cluster).     
%                                                                         
% There are 10 data sets in the DIMACS10 collection:                      
%                                                                         
% Kronecker:  synthetic graphs from the Graph500 benchmark                
% dyn-frames: frames from a 2D dynamic simulation                         
% Delaunay:   Delaunay triangulations of random points in the plane       
% coauthor:   citation and co-author networks                             
% streets:    real-world street networks                                  
% Walshaw:    Chris Walshaw's graph partitioning archive                  
% matrix:     graphs from the UF collection (not added here)              
% random:     random geometric graphs (random points in the unit square)  
% clustering: real-world graphs commonly used as benchmarks               
% numerical:  graphs from numerical simulation                            
%                                                                         
% Some of the graphs already exist in the UF Collection.  In some cases,  
% the original graph is unsymmetric, with values, whereas the DIMACS      
% graph is the symmetrized pattern of A+A'.  Rather than add duplicate    
% patterns to the UF Collection, a MATLAB script is provided at           
% http://www.cise.ufl.edu/research/sparse/dimacs10 which downloads        
% each matrix from the UF Collection via UFget, and then performs whatever
% operation is required to convert the matrix to the DIMACS graph problem.
% Also posted at that page is a MATLAB code (metis_graph) for reading the 
% DIMACS *.graph files into MATLAB.                                       
%                                                                         
%                                                                         
% clustering:  Clustering Benchmarks                                      
%                                                                         
% These real-world graphs are often used as benchmarks in the graph       
% clustering and community detection communities.  All but 4 of the 27    
% graphs already appear in the UF collection in other groups.  The        
% DIMACS10 version is always symmetric, binary, and with zero-free        
% diagonal.  The version in the UF collection may not have those          
% properties, but in those cases, if the pattern of the UF matrix         
% is symmetrized and the diagonal removed, the result is the DIMACS10     
% graph.                                                                  
%                                                                         
% DIMACS10 graph:                 new?   UF matrix:                       
% ---------------                 ----   -------------                    
% clustering/adjnoun                     Newman/adjoun                    
% clustering/as-22july06                 Newman/as-22july06               
% clustering/astro-ph                    Newman/astro-ph                  
% clustering/caidaRouterLevel      *     DIMACS10/caidaRouterLevel        
% clustering/celegans_metabolic          Arenas/celegans_metabolic        
% clustering/celegansneural              Newman/celegansneural            
% clustering/chesapeake            *     DIMACS10/chesapeake              
% clustering/cnr-2000                    LAW/cnr-2000                     
% clustering/cond-mat-2003               Newman/cond-mat-2003             
% clustering/cond-mat-2005               Newman/cond-mat-2005             
% clustering/cond-mat                    Newman/cond-mat                  
% clustering/dolphins                    Newman/dolphins                  
% clustering/email                       Arenas/email                     
% clustering/eu-2005                     LAW/eu-2005                      
% clustering/football                    Newman/football                  
% clustering/hep-th                      Newman/hep-th                    
% clustering/in-2004                     LAW/in-2004                      
% clustering/jazz                        Arenas/jazz                      
% clustering/karate                      Arenas/karate                    
% clustering/lesmis                      Newman/lesmis                    
% clustering/netscience                  Newman/netscience                
% clustering/PGPgiantcompo               Arenas/PGPgiantcompo             
% clustering/polblogs                    Newman/polblogs                  
% clustering/polbooks                    Newman/polbooks                  
% clustering/power                       Newman/power                     
% clustering/road_central          *     DIMACS10/road_central            
% clustering/road_usa              *     DIMACS10/road_usa                
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