Since Kronecker Product Graph Model (KPGM) was intro-duced, it has been widely used to model real networks. The characteristics of the model specially its single fractal struc-ture have made KPGM one of the most important algorithm of the last years. However, the utilization of a single fractal structure decreases the potential of KPGM by limiting the graph space covered by the model. In this paper, we propose a new generalization of KPGM, called block-KPGM. This new model expands the graph space covered for KPGM uti-lizing multiple fractal structures, generating networks with characteristics not generated by previous Kronecker mod-els. We evaluate the block-KPGM by comparing it against two types of Kronecker models. We compare the cumula-tive distribution functions over three characteristics to show that block-KPGMs are able to produce networks that more closely match real-world graphs, reducing the multidimen-sional Kolgomorov-Smirnov distance between 11 % to 63%.

Cited by 0

Block designs and graph imbeddings

Arthur T. White · Journal of Combinatorial Theory Series B · 1978

Cited by 25

Block designs and graph theory

Lindsay Paterson · ERA · 1981

Cited by 0Open access

Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph

B. Satyanarayana, Srinivasulu Devanaboina, Syam Prasad Kuncham et al. · International Journal of Computer Applications · 2012

We considersemitotal-block graph, total-block graph of a graph G (respectively, denoted as T b (G), T B (G)). We prove that the number of edges in a semitotal-block graph of a given graph G is equal to

Cited by 2Open access

THE SEMI-IMAGE NEIGHBOURHOOD BLOCK GRAPH OF A GRAPH

Kulli, V. R, K. M. Niranjan · SPIRE - Sciences Po Institutional REpository · 2020

International audience

Cited by 1

The block energy of a graph

B. Sharada, Mohammad Issa Sowaity, A. M. Naji · Online Journal of Analytic Combinatorics · 2019

In this paper, we introduce the concept block matrix (B-matrix) of a graph $ G $, and obtain some coefficients of the characteristic polynomial $ \phi(G, \mu) $ of the B-matrix of $ G $. The block energy $ E_B(G) $ is established. Further upper and lower bounds for $ E_B(G) $ are obtained. In addition, we define a uni-block graph. Some properties and new bounds for the block energy of the uni-block graph are presented.

Cited by 0Open access

Block digraph of a directed graph

H. M. Nagesh, M. C. Mahesh Kumar · Open Journal of Mathematical Sciences · 2018

Let D be a connected digraph of order n (n 3) and let

Cited by 19Open access

The square of a block graph

Van Bang Lê, Nguyen Ngoc Tuy · Discrete Mathematics · 2009

Cited by 26

Block Statistics in Subcritical Graph Classes

Dimbinaina Ralaivaosaona, Clément Requilé, Stephan Wagner · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2020

We study block statistics in subcritical graph classes; these are statistics that can be defined as the sum of a certain weight function over all blocks. Examples include the number of edges, the number of blocks, and the logarithm of the number of spanning trees. The main result of this paper is a central limit theorem for statistics of this kind under fairly mild technical assumptions.

Cited by 0Open access

Universal Graph Compression: Stochastic Block Models

Alankrita Bhatt, Ziao Wang, Chi Wang et al. · 2021

Motivated by the prevalent data science applications of processing large-scale graph data such as social networks, web graphs, and biological networks, as well as the high I/O and communication costs of storing and transmitting such data, this paper investigates universal compression of data appearing in the form of a labeled graph. In particular, we consider a widely used random graph model, stochastic block model (SBM), which captures the clustering effects in social networks. A universal graph compressor is proposed, which achieves the optimal compression rate for a wide family of SBMs with edge probabilities from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O$</tex> (1) to Ω(1/ <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2-∊</sup> ) for any 0 < ∊ < 1. Existing universal compression techniques are developed mostly for stationary ergodic one-dimensional sequences with entropy linear in the number of variables. However, the adjacency matrix of SBM has complex two-dimensional correlations and sublinear entropy in the sparse regime. These challenges are alleviated through a carefully designed transform that converts two-dimensional correlated data into almost i.i.d. blocks. The blocks are then compressed by a Krichevsky-Trofimov compressor, whose length analysis is generalized to arbitrarily correlated processes with identical marginals.

Cited by 6

SECOND POWER OF DIRECTED BLOCK GRAPH

M M Massoumi, Farhad Hosseinzadeh Lotfi, M Rostami Mal Khalife et al. · 2010

Cited by 0

Streaming graph challenge: Stochastic block partition

Edward K. Kao, Vijay Gadepally, M. Hurley et al. · arXiv (Cornell University) · 2017

An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard, but existing relaxation methods provide reasonable approximate solutions that can be scaled for large graphs. Competitive benchmarks and challenges have proven to be an effective means to advance state-of-the-art performance and foster community collaboration. This paper describes a graph partition challenge with a baseline partition algorithm of sub-quadratic complexity. The algorithm employs rigorous Bayesian inferential methods based on a statistical model that captures characteristics of the real-world graphs. This strong foundation enables the algorithm to address limitations of well-known graph partition approaches such as modularity maximization. This paper describes various aspects of the challenge including: (1) the data sets and streaming graph generator, (2) the baseline partition algorithm with pseudocode, (3) an argument for the correctness of parallelizing the Bayesian inference, (4) different parallel computation strategies such as node-based parallelism and matrix-based parallelism, (5) evaluation metrics for partition correctness and computational requirements, (6) preliminary timing of a Python-based demonstration code and the open source C++ code, and (7) considerations for partitioning the graph in streaming fashion. Data sets and source code for the algorithm as well as metrics, with detailed documentation are available at GraphChallenge.org.

Cited by 68Open access

The square of a block graph

Van Bang Le, et al. · 2009

Cited by 0

Jimple block program dependence graph example.

Fahmi H. Quradaa (17896527), Sara Shahzad (14570660), Rashad Saeed (18536093) et al. · Figshare · 2024

<div><p>In software development, it’s common to reuse existing source code by copying and pasting, resulting in the proliferation of numerous code clones—similar or identical code fragments—that detrimentally affect software quality and maintainability. Although several techniques for code clone detection exist, many encounter challenges in effectively identifying semantic clones due to their inability to extract syntax and semantics information. Fewer techniques leverage low-level source code representations like bytecode or assembly for clone detection. This work introduces a novel code representation for identifying syntactic and semantic clones in Java source code. It integrates high-level features extracted from the Abstract Syntax Tree with low-level features derived from intermediate representations generated by static analysis tools, like the Soot framework. Leveraging this combined representation, fifteen machine-learning models are trained to effectively detect code clones. Evaluation on a large dataset demonstrates the models’ efficacy in accurately identifying semantic clones. Among these classifiers, ensemble classifiers, such as the LightGBM classifier, exhibit exceptional accuracy. Linearly combining features enhances the effectiveness of the models compared to multiplication and distance combination techniques. The experimental findings indicate that the proposed method can outperform the current clone detection techniques in detecting semantic clones.</p></div>

Cited by 0Open access

Graph Learning-Based Arithmetic Block Identification

Zhuolun He, Ziyi Wang, Chen Bai et al. · 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD) · 2021

Arithmetic block identification in gate-level netlist is an essential procedure for malicious logic detection, functional verification, or macro-block optimization. We argue that existing methods suffer either scalability or performance issues. To address the problem, we propose a graph learning-based solution that promises to extract desired logic components from a complete design netlist. We further design a novel asynchronous bidirectional graph neural network (ABGNN) dedicated to representation learning on directed acyclic graphs. Experimental results on open-source RISC-V CPU designs demonstrate that our proposed solution significantly outperforms several state-of-the-art arithmetic block identification flows.

Cited by 39