Publication

array(14 items)
   uid => 931 (integer)
   title => 'Cavity approach for the approximation of spectral density of graphs with het
      erogeneous structures' (97 chars)
   abstract => 'Graphs have become widely used to represent and study social, biological, an
      d technological systems. Statistical methods to analyze empirical graphs wer
      e proposed based on the graph's spectral density. However, their running tim
      e is cubic in the number of vertices, precluding direct application to large
       instances. Thus, efficient algorithms to calculate the spectral density bec
      ome necessary. For sparse graphs, the cavity method can efficiently approxim
      ate the spectral density of locally treelike undirected and directed graphs.
       However, it does not apply to most empirical graphs because they have heter
      ogeneous structures. Thus, we propose methods for undirected and directed gr
      aphs with heterogeneous structures using a new vertex's neighborhood definit
      ion and the cavity approach. Our methods' time and space complexities are O(
      |E|h_{max}^{3}t) and O(|E|h_{max}^{2}t), respectively, where |E| is the numb
      er of edges, h_{max} is the size of the largest local neighborhood of a vert
      ex, and t is the number of iterations required for convergence. We demonstra
      te the practical efficacy by estimating the spectral density of simulated an
      d real-world undirected and directed graphs.' (1184 chars)
   authors => array(3 items)
      0 => array(3 items)
         last_name => 'Guzman' (6 chars)
         first_name => 'Grover E.  C.' (13 chars)
         sorting => 1 (integer)
      1 => array(3 items)
         last_name => 'Stadler' (7 chars)
         first_name => 'Peter Florian' (13 chars)
         sorting => 2 (integer)
      2 => array(3 items)
         last_name => 'Fujita' (6 chars)
         first_name => 'André' (6 chars)
         sorting => 3 (integer)
   type => '0' (1 chars)
   keywords => '' (0 chars)
   year => 2024 (integer)
   affiliation => 1 (integer)
   link_paper => '' (0 chars)
   link_supplements => '' (0 chars)
   file_published => 0 (integer)
   journal => 'Physical Review E' (17 chars)
   doi => '10.1103/PhysRevE.109.034303' (27 chars)
   preprint => '-1' (2 chars)