Graph Theory

In the book the authors define, describe, and develop the notion of complex valued graphs, complex neutrosophic valued graphs, and mod complex valued graphs in a systematic way. However complex neural networks have been analyzed and studied as early as 2003. This book gives several applications of them in medical diagnosis, soft computing, and so on.
This will be of interest of researchers in these areas.

Community detection is a major issue in network analysis. This paper combines a socio-historical approach with an experimental reconstruction of programs to investigate the early automation of clique detection algorithms, which remains one of the unsolved NP-complete problems today. The research led by the archaeologist Jean-Claude Gardin from the 1950s on non-numerical information and graph analysis is retraced to demonstrate the early contributions of social sciences and humanities. The limited recognition and reception of Gardin’s innovative computer application to the humanities are addressed through two factors, in addition to the effects of historiography and bibliographies on the recording, discoverability, and reuse of scientific productions: 1) funding policies, evidenced by the transfer of research effort on graph applications from temporary interdisciplinary spaces to disciplinary organizations related to the then-emerging field of computer science; and 2) the erratic careers of algorithms, in which efficiency, flaws, corrections, and authors’ status, were determining factors.

This study is motivated by the unexpected failure of a network-based system during the performance of corrective maintenance. This incident highlights the importance of incorporating network connectivity analysis in maintenance planning. This study shows that it is crucial to consider network connectivity when planning maintenance. Procedures to conduct maintenance planning with network connectivity consideration is proposed and discussed

This paper introduces a new method for the session construction problem, which is the first main step of the web usage mining process. The proposed method is capable of extracting all possible maximal navigation sequences of web users. Through experiments, it is shown that when our new technique is used, it outperforms previous approaches in web usage mining applications such as next-page prediction.

The Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by [Thomassen '89 & '93], and it is known to be fixed-parameter tractable. However, the approximability of the Euler genus is wide open. While the existence of an O(1)-approximation is not ruled out, only an O(sqrt(n))-approximation [Chen, Kanchi, Kanevsky '97] is known even in bounded degree graphs. In this paper we give a polynomial-time algorithm which on input a bounded-degree graph of Euler genus g, computes a drawing into a surface of Euler genus poly(g, log(n)). Combined with the upper bound from [Chen, Kanchi, Kanevsky '97], our result also implies a O(n^(1/2 - alpha))-approximation, for some constant alpha>0. Using our algorithm for approximating the Euler genus as a subroutine, we obtain, in a unified fashion, algorithms with approximation ratios of the form poly(OPT, log(n)) for several related problems on bounde...

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the ...

We study a very large family of graphs, the members of which comprise disjoint paths of
cliques with extremal cliques identified. This broad characterisation naturally generalises
those of various smaller families of graphs having well-known chromatic polynomials. We
derive a relatively simple formula for an arbitrary member of the subfamily consisting of
those graphs whose constituent clique-paths have at least one trivial extremal clique, and
use this formula to show that the set of all non-integer chromatic roots of these graphs is
closed under multiplication by natural numbers. A well-known result of Sokal then leads
to our main result, which is that there exists a set of chromatic roots which is closed under
positive integer multiplication in addition to being dense in the complex plane. Our findings
lend considerable weight to a conjecture of Cameron, who has suggested that this closure
property may be a generic feature of the chromatic polynomial. We also hope that the
formula we provide will be of use to those computing with chromatic polynomials.

Self-organizing software generation teams are increasing due to the more innovation and convivence these networks provide. This article focuses on the security evaluation of the open-source software development (OSSD) team. A newly generated formula for assessing the network security of a collaborative network is proposed and evaluated. For this purpose, we take advantage of graph theory criteria. Using this measure, if the developer's network is vulnerable in some parts, the guideline can be used for attracting/strengthening the ties in OSSD.

Comparative network analysis is an emerging line of research that provides insights into the structure and dynamics of networks by finding similarities and discrepancies in their topologies. Unfortunately, comparing networks directly is not feasible on large scales. Existing works resort to representing networks with vectors of features extracted from their topologies and employ various distance metrics to compare between these feature vectors. In this paper, instead of relying on feature vectors to represent the studied networks, we suggest fitting a network model (such as Kronecker Graph) to encode the network structure. We present the directed fitting-distance measure, where the distance from a network A to another network B is captured by the quality of B's fit to the model derived from A. Evaluation on five classes of real networks shows that KronFit based distances perform surprisingly well.

Synthesis of asynchronous circuits from Signal Transition Graphs (STGs) involves resolving state coding conflicts. The refinement process is generally done automatically using heuristics and often produces sub-optimal solutions, which have to be corrected manually. This paper presents a framework for an interactive refinement process aimed to help the designer. It is based on the visualization of conflict cores, i.e., sets of transitions causing coding conflicts, which are represented at the level of finite and complete prefixes of STG unfoldings.

The regular number of a graph\(G\) denoted by\(reg (G)\) is the minimum number of subsets into which the edge set of\(G\) can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an open problem in Ganesan et al.(J Discrete Math Sci Cryptogr 15 (2–3): 49–157, 2012) about the complexity of determining the regular number of graphs. We show that computation of the regular number for connected bipartite graphs is NP-hard. Furthermore, we show that, determining ...