Topological structure analysis in directed network

Proceedings of the 13th …, 2011

Abstract:-This paper is focused on the description as to how to find all giant connected components in directed network by means of computer technology. For experimental testing, the growing complex networks with preferential linking were used within this research. ...

2016

Complex Networks are massive in size and their interactions are complex. Therefore, it is difficult to represent a network partially. To represent a network partially, we need to study the topology and topological properties of the network. The goal of studying complex networks is not only to examine the underlying structure of complex systems, but also to learn how we can control them more efficiently. In this paper we are analyzing the properties of different network models of complex networks with the real dataset.

International Journal of Computer Applications, 2014

In late 1950s, two mathematicians discovered a network with complex topology by random graph theory. Complex networks have received great attention in past few decades. Many studies have been done on complex networks and many are still in progress. Complex Networks are the networks which can be seen in real as well as in technological systems. They have nodes and these nodes are connected by various links. They are called complex networks because of the underlying complex architecture and complex topology. In this paper, our goal is to study the complex networks and various basic terms related to complex networks like mutual behavior between real-networks and complex networks, average path length, clustering coefficient, degree distribution. Designing and analyzing the behavior and dynamics of a complex networked system are also discussed. Hence, A complex networked system can helps us in: understanding the efficiency of new security approaches for computer networks, improving the design of computer networks to make it more robust and resilience against errors and failures occurred in system, understanding how population will respond to introduction of new nodes in system, detecting subtle vulnerabilities, and also detecting catastrophic failures in power grid.

Crucial nodes in a network refer to those nodes that their existence is so important in preserving topological structure of the network and they independently determine the network structure. In this study I introduced and proposed several mathematical methods for identifying crucial nodes in networks. They fall into three categories, node perturbation, network analysis, and network dynamics. Node perturbation methods include adjacency matrix index, degree or flow change index, node perturbation index, etc. Network dynamics methods include network evolution modeling, etc. Network analysis methods include node degree, criticality index, branch flourishing index, node importance index, etc. Advantages and advantages of these methods were discussed. Finally, I suggested that some of these methods may also be used to identify crucial links (connections) in networks. In this case, the change of a link refers to presence/absence of a link, or change of flow in the link, etc.

ArXiv, 2010

Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an acyclic network allows finding structural properties of the network. With our approach one can find the communities and key nodes in complex networks. Also we propose a new parameter of complex networks which can mark most vulnerable nodes of the system. The proposed algorithm can be applied to finding communities and bottlenecks in general complex networks.

• Proposed conjectural link concept — link that should be existing but there is not. • Introduced a parameter that allows ranking the Conjectural Link. • Two methods of conjectural links detection are proposed. • Conjectural links can be used for recovery of partially destroyed Complex Networks. • Several examples of conjectural links detection in real networks are reviewed. a b s t r a c t This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the characteristics of its topology. It is possible, for example, when in the formal description of the network some connections are skipped due to errors, deliberately hidden or withdrawn (e.g. in the case of partial destruction of the network). Introduced a parameter that allows ranking the Conjectural Link. The more this parameter — the more likely that this connection should be present in the network. This paper presents a method of recovery of partially destroyed Complex Networks using Conjectural Links finding. Presented two methods of finding the node pairs that are not linked directly to one another, but have a great possibility of Conjectural Link communication among themselves: a method based on the determination of the resistance between two nodes, and method based on the computation of the lengths of routes between two nodes. Several examples of real networks are reviewed and performed a comparison to know network links prediction methods, not intended to find the missing links in already formed networks.

Physical Review E, 2010

To identify communities in directed networks, we propose a generalized form of modularity in directed networks by presenting the quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed networks by optimizing our modified modularity. Also, a model network, which can be used as a benchmark network in further community studies, is proposed to verify our method. Our method is supposed to find communities effectively in citationor reference-based directed networks.

Journal of Statistical Physics, 2006

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.

Eprint Arxiv 1010 1864, 2010

Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an acyclic network allows finding structural properties of the network. With our approach one can find the communities and key nodes in complex networks. Also we propose a new parameter of complex networks which can mark most vulnerable nodes of the system. The proposed algorithm can be applied to finding communities and bottlenecks in general complex networks.

2004

Abstract Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science.