The many faces of graph dynamics

Abstract

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time.Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a "one fits it all" model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions.To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (nonanonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs.We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Towards Granular Knowledge Structures: Comparison of Different Approaches

“…Existing common alternatives for this metric are concept frequency in the text (TFIDF), fuzzy concept lattices [9] Example or historic evolution of concept centrality in the given corpus [10]. A more recent trend, usable in case where concepts can be mapped in a metric space, relies on identification of dense areas and their association with a representative concept as centroid [11] [12].…”

Finding Structure in Dynamic Networks

“…(The project was not retained and we started collaborating on another topic.) This kind of concepts, including also temporal betweenness or closeness (which we expressed in the TVG formalism in [133]), received a lot of attention lately (see e.g., [125,130]).…”