On multidimensional network measures ⋆ Matteo Magnani, Anna Monreale, Giulio Rossetti, and Fosca Giannotti KDDLab, ISTI, CNR, via G. Moruzzi 1, 56124 Pisa, Italy name.surname @isti.cnr.it Discussion Paper [1, 2] Abstract. Networks, i.e., sets of interconnected entities, are ubiquitous, spanning disciplines as diverse as sociology, biology and computer sci- ence. The recent availability of large amounts of network data has thus provided a unique opportunity to develop models and analysis tools ap- plicable to a wide range of scenarios. However, real-world phenomena are often more complex than existing graph data models. One relevant ex- ample concerns the numerous types of social relationships (or edges) that can be present between individuals in a social network. In this short pa- per we present a unified model and a set of measures recently developed to represent and analyze network data with multiple types of edges. Keywords: Multidimensional networks, multi-layer networks, central- ity measures 1 Introduction Recent years have witnessed a dramatic increase of interest in the modeling power provided by network models, representing the relationships between ab- stract entities. This interest has been determined by the wide applicability of these models to several disciplines, including social network analysis and statis- tics, biology, physics and economics [3–5], and by the contemporary availability of large network datasets, a primary example being online social networks. The interdisciplinary character of this problem has influenced recent devel- opments in the field of computer science, where simple graph models have been enriched with additional information to conform to the representation needs re- quired in other disciplines. For example, in the context of social network data one important feature to be considered is the differentiation between several kinds of connections: the relationship between two individuals is a complex phenomenon that cannot be simplified by reducing it to a simple edge between two nodes in a graph. Working together, being friend or having a connection on LinkedIn are very different kinds of ties. They all contribute to the definition of a complex so- cial relationship, but cannot be merged and downgraded to a mono-dimensional concept. ⋆ This work has been partly supported by FIRB project RBFR107725.