ABACUS: frequent pAttern mining-BAsed Community discovery in mUltidimensional networkS

Abstract

Community Discovery in complex networks is the problem of detecting, for each node of the network, its membership to one of more groups of nodes, the communities, that are densely connected, or highly interactive, or, more in general, similar, according to a similarity function. So far, the problem has been widely studied in monodimensional networks, i.e. networks where only one connection between two entities may exist. However, real networks are often multidimensional, i.e., multiple connections between any two nodes may exist, either reflecting different kinds of relationships, or representing different values of the same type of tie. In this context, the problem of Community Discovery has to be redefined, taking into account multidimensional structure of the graph. We define a new concept of community that groups together nodes sharing memberships to the same monodimensional communities in the different single dimensions. As we show, such communities are meaningful and able to group nodes even if they might not be connected in any of the monodimensional networks. We devise ABACUS (frequent pAttern mining-BAsed Community discoverer in mUltidimensional networkS), an algorithm that is able to extract multidimensional communities based on the extraction of frequent closed itemsets from monodimensional community memberships. Experiments on two different real multidimensional networks confirm the meaningfulness of the introduced concepts, and open the way for a new class of algorithms for community discovery that do not rely on the dense connections among nodes.

The structure and dynamics of multilayer networks

“…Another mathematical model capturing multiple different relations that act at the same time is that of multidimensional networks [14,20,[30][31][32][33][63][64][65][66][67]. In a multidimensional network, a pair of entities may be linked by different kinds of links.…”

An Approach to Data Analysis in 5G Networks

“…The first one aims to determine the evolution of the HoN metrics, hence it mainly implements exponential smoothing algorithms [48] and autoregressive models [49]. On the other hand, the evolution of graphs is predicted in order to anticipate the discovery of new elements [50] and facilitate the management of resources [51]. • Adaptive Thresholding: establishes measures to approximate when the forecast errors must be taken into account when identifying symptoms.…”

Discovering Dynamic Communities in Interaction Networks

“…Similar recent works apply concepts of Laplacian dynamics [46] and frequent pattern mining [10] to ensure coherence and sufficiency of communities found in a sequence of graph snapshots. Another example of snapshot-based approach is based on state-of-the-art spectral clustering extended by consistency constraints [17] or adaptive forgetting factor [62].…”

“…Furthermore, the densest subgraph can be always found in the network, spliced by the whole time interval [0, T ]. On the other hand, if we increase the allowed size of |T | to K = 3, then we can cover community C c with nodes [5,7], [10,10]}, and span(T c ) ≤ 3, which is reasonably small in the scale of our toy example. Thus, by introducing and varying constraints values we may obtain more meaningful results.…”