Foundations of Multidimensional Network Analysis

Abstract

Abstract-Complex networks have been receiving increasing attention by the scientific community, thanks also to the increasing availability of real-world network data. In the last years, the multidimensional nature of many real world networks has been pointed out, i.e. many networks containing multiple connections between any pair of nodes have been analyzed. Despite the importance of analyzing this kind of networks was recognized by previous works, a complete framework for multidimensional network analysis is still missing. Such a framework would enable the analysts to study different phenomena, that can be either the generalization to the multidimensional setting of what happens in monodimensional network, or a new class of phenomena induced by the additional degree of complexity that multidimensionality provides in real networks. The aim of this paper is then to give the basis for multidimensional network analysis: we develop a solid repertoire of basic concepts and analytical measures, which takes into account the general structure of multidimensional networks. We tested our framework on a real world multidimensional network, showing the validity and the meaningfulness of the measures introduced, that are able to extract important, nonrandom, information about complex phenomena.

Event-based Archaeological Registration Principles

“…7); we asked for instance to what amount the various networks overlap each other, more precisely: if two nodes, which are directly connected in one network, are also connected in one of the other or in all other networks (Maoz 2011, 39-41, 333-364;Munson and Macri 2009, 435-436;; cf. also Berlingero et al 2011). We determined the percentage of overlap of links between the three networks with the same number of nodes (streets, state, church) by means of a comparison of the matrices of the networks (Fig.…”

Visual Analysis of Dynamic Networks Using Change Centrality

“…In general, new metrics have been proposed for multidimensional networks, in which the attributes of nodes and links chosen as dimensions are not necessarily referring to time, but for example to the type of relation in multi-relational networks. Berligerio et al [16] extend the degree centrality from the monodimensional to the multidimensional case and introduce new metrics, namely dimension relevance, dimension connectivity and dimension correlation. Brodka et al [17] define a cross-layer degree, that is an aggregated node centrality measure across the relations of a multi-relational network.…”

Towards the characterization of realistic models

“…E2 T3 T4 T2 T5 T6 T1 T1 T2 T3 T5 T6 T4 (a) Light switch statechart. To calculate the metrics of models, we map them to multidimensional graphs [5]. A multidimensional graph is defined as G = (V, E, D), where V is the set of nodes (vertices), E is the set of directed edges between the nodes, and D represents the set of dimensions that label the edges.…”