Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

On the Computation of Centrality Metrics for Network Security in Mesh Networks

Abstract: Betweenness centrality is a popular metric in social science, and recently it was adopted also in computer science. Betweenness identifies the node, or the nodes, that are most suitable to perform critical network functions, such as firewalling and intrusion detection. However, computing centrality is resource-demanding, we can not give for granted that it can be computed in real time at every change in the network topology. This is especially true in mesh networks that generally use devices with few computation resources. This paper shows that using the fastest state-of-the-art heuristic algorithm it is indeed possible to compute network centrality even in real, low-power networking hardware in a network made of up to 1000 nodes. Not only, observing the behavior of a real mesh network it shows that centrality does not need to be updated at every topology change, but it can be safely re-computed with an interval in the order of the tens of minutes. Our findings confirms that centrality can be effectively and successfully used as a building block for security functions in mesh networks.

Relating network topology to the robustness of centrality measures

Abstract: : This paper reports on a simulation study of social networks that investigated how network topology relates to the robustness of measures of system-level node centrality. This association is important to understand as data collected for social network analysis is often somewhat erroneous and may, to an unknown degree, misrepresent the actual true network. Consequently, the values for measures of centrality calculated from the collected network data may also vary somewhat from those of the true network, possibly leading to incorrect suppositions. To explore the robustness, i.e., sensitivity, of network centrality measures in this circumstance, we conduct Monte Carlo experiments whereby we generate an initial network, perturb its copy with a specific type of error, then compare the centrality measures from two instances. We consider the initial network to represent a true network, while the perturbed represents the observed network. We apply a six-factor full-factorial block design for the overall methodology. We vary several control variables (network topology, size and density, as well as error type, form and level) to generate 10,000 samples each from both the set of all possible networks and possible errors within the parameter space. Results show that the topology of the true network can dramatically affect the robustness profile of the centrality measures. We found that across all permutations that cellular networks had a nearly identical profile to that of uniform-random networks, while the core-periphery networks had a considerably different profile. The centrality measures for the core-periphery networks are highly sensitive to small levels of error, relative to uniform and cellular topologies. Except in the case of adding edges, as the error increases, the robustness level for the 3 topologies deteriorates and ultimately converges.

Distributed location of the critical nodes to network robustness based on spectral analysis

Abstract: We propose a methodology to locate the most critical nodes to network robustness in a fully distributed way. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a limited neighborhood around each node in the network. We also present a procedure allowing the navigation from any node towards a critical node following only local information computed by the proposed algorithm. Experimental results confirm the effectiveness of our proposal considering networks of different scales and topological characteristics.

A New Method for Identifying the Central Nodes in Fuzzy Cognitive Maps using Consensus Centrality Measure

Abstract: The Fuzzy Cognitive Map (FCM) provides a robust model for knowledge representation. FCM is a fuzzy signed weighted directed graph that depicts the knowledge of the domain as nodes representing the factors of the domain and arcs representing the connections among these factors. The centrality of a node in FCM, also called the importance of a node in this paper, is considered the most important index of all the graph theory indices applying to FCM which helps decision makers in analysing their FCM models. By finding the centrality values of the nodes in FCM, the important (central) nodes, which are the focal point for decision makers, are determined. The highest centrality value of a node in FCM is the most important one. Little research has addressed the centrality of the nodes in an FCM using only the degree centrality measure. The degree centrality measure only accounts for the direct connections of the node. Although the degree centrality index is considered an important measure in determining the centrality of a node in an FCM, it is not sufficient and has significant shortcomings; it ignores the importance of the indirect connections, the role of the node's position and flow of information through that node, i.e., how a node is close to other nodes and how the node contributes to the flow of information (communication control) through that node. In the literature, there are other centrality measures that can handle direct and indirect connections to determine the central nodes in a directed graph. This paper presents a new method for identifying the central nodes in an FCM. In order to achieve that, we provide, in addition to the degree measure, new important measures to overcome the above drawbacks. These new centrality measures are: betweenness and closeness measures. In this paper, we calculate and normalize the three centrality measures values for each node in the FCM. These values are then transformed into linguistic terms using 2-tuple fuzzy linguistic representation model. We use the 2-tuple model because it describes the granularity of uncertainty of the fuzzy sets and avoids the loss of information resulted from the imprecision and normalization of the measures. The calculated centrality measures values for each node in the FCM are then aggregated using a 2-tuple fuzzy fusion approach to obtain consensus centrality measure. The resulting aggregated values are then ranked in descending order to identify the most central nodes in the FCM, and this would improve the decision-making and help in simplify the FCM by removing the least important nodes from it. Finally, a list of future works related to this paper is suggested.