Mining (maximal) Span-cores from Temporal Networks

Galimberti, Edoardo; Barrat, Alain; Bonchi, Francesco; Cattuto, Ciro; Gullo, Francesco

doi:10.1145/3269206.3271767

Cited by 43 publications

(51 citation statements)

References 46 publications

(62 reference statements)

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“…In [52] cores in a temporal graph are considered to exist in temporal internals ∆ and are named span-cores. The authors then make the the note that a span-core at k, ∆ is contained in a span core k, ∆ if k ≤ k & ∆ ⊆ ∆.…”

Section: Core Decomposition In Dynamic Environmentsmentioning

confidence: 99%

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The core decomposition of networks: theory, algorithms and applications

et al. 2019

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The core decomposition of networks has attracted significant attention due to its numerous applications in real-life problems. Simply stated, the core decomposition of a network (graph) assigns to each graph node v, an integer number c(v) (the core number), capturing how well v is connected with respect to its neighbors. This concept is strongly related to the concept of graph degeneracy, which has a long history in Graph Theory. Although the core decomposition concept is extremely simple, there is an enormous interest in the topic from diverse application domains, mainly because it can be used to analyze a network in a simple and concise manner by quantifying the significance of graph nodes. Therefore, there exists a respectable number of research works that either propose efficient algorithmic techniques under different settings and graph types or apply the concept to another problem or scientific area. Based on this large interest in the topic, in this survey, we perform an in-depth discussion of core decomposition, focusing mainly on: i) the basic theory and fundamental concepts, ii) the algorithmic techniques proposed for computing it efficiently under different settings, and iii) the applications that can benefit significantly from it.

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Section: Core Decomposition In Dynamic Environmentsmentioning

confidence: 99%

“…An interesting application of temporal cores is found in the aforementioned work of [52] (Dynamic Graphs) for the detection of anomalous contacts in social networks. Besides the extensions of the k-core structure into temporal graphs, the evolution of degeneracy has also been studied as a property through time (e.g.…”

Section: Temporal Evolutionmentioning

confidence: 99%

The core decomposition of networks: theory, algorithms and applications

et al. 2019

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“…Here, we contribute to the first, most theoretical step of this line of research by proposing a novel type of candidate structures for idealized targeted interventions: the span-cores of a temporal network. The span-cores are structures that we recently introduced 26 to decompose a temporal network into hierarchies of subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. They could thus in temporal contact networks be interpreted as long-lasting groups of interacting individuals.…”

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confidence: 99%

“…In temporal networks, the span-cores are defined 26 as temporal subgraphs as follows: a span-core C of order k is defined on an interval of contiguous timestamps, such that all nodes in C have at all timestamps of that interval at least k stable neighbours in C (i.e., the links to these nodes are present during all timestamps of the interval). Each span-core is thus characterized by two quantities: its order and its duration (the length of the interval on which it is defined).…”

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confidence: 99%

Relevance of temporal cores for epidemic spread in temporal networks

Ciaperoni

Galimberti

Bonchi

et al. 2020

Sci Rep

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temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing spancores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to include influential spreaders. A large variety of systems find a convenient representation as networks of interactions between components. Network representations have indeed proved to be useful to understand the structure and dynamics of systems as diverse as transportation infrastructures or social networks, as well as to describe processes occurring on top of them, such as information diffusion, epidemic spread, synchronization, etc 1. A large body of work aims in particular at understanding how the network's features impact the outcome of processes taking place on top of them, with the ambition of devising control and prediction capabilities. For instance, several methods have been put forward to identify the nodes of a network that play a more important role in a spreading process, either because they are "influencers" able to widely spread an information, or because they are "sentinels" with a high probability to be reached by a disease in its early stages and thus can give an early warning, or because their immunization is likely to hinder the spread 2-11. Such a task becomes even more complex when dealing with temporal networks, in which edges between nodes can appear and disappear on different time scales. The recent availability of time-resolved data sets of interactions has pushed network science beyond the static graph representation and has led to the development of the field of temporal networks 12,13. The temporal dimension can yield non-trivial temporal features such as broad distributions of interaction times and of inter-event times ("burstiness"), heterogeneous activity distributions, causality constraints, and overall a broader diversity of activity/connectivity patterns tha...

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“…Such "static" catalogues of patterns of firing partially fail at highlighting that the temporally coordinated firing of nodes gives rise to a dynamics of functional links 10-12 , i.e., to a temporal network [13][14][15] .The temporal network framework has recently emerged in order to take into account that for many systems, a static network representation is only a first approximation that hides very important properties. This has been made possible by the availability of temporally resolved data in communication and social networks in particular [16][17][18][19] : studies of these data have uncovered features such as broad distributions of contact or inter-contact times (burstiness) between individuals 16, 17 , multiple temporal and structural scales [19][20][21] , and a rich array of intrinsically dynamical structures that could not be unveiled within a static network framework [22][23][24][25] . Taking into account temporality has moreover been shown to have a strong impact in processes taking place on networks, in particular the propagation of diseases or of information 18,26,27 .…”

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confidence: 99%

Dynamic core periphery structure of information sharing networks in entorhinal cortex and hippocampus

Pedreschi

Bernard

Clawson

et al. 2020

Preprint

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ABSTRACTNeural computation is associated with the emergence, reconfiguration and dissolution of cell assemblies in the context of varying oscillatory states. Here, we describe the complex spatio-temporal dynamics of cell assemblies through temporal network formalism. We use a sliding window approach to extract sequences of networks of information sharing among single units in hippocampus and enthorinal cortex during anesthesia and study how global and node-wise functional connectivity properties evolve along time and as a function of changing global brain state (theta vs slow-wave oscillations). First, we find that information sharing networks display, at any time, a core-periphery structure in which an integrated core of more tightly functionally interconnected units link to more loosely connected network leaves. However the units participating to the core or to the periphery substantially change across time-windows, with units entering and leaving the core in a smooth way. Second, we find that discrete network states can be defined on top of this continuously ongoing liquid core-periphery reorganization. Switching between network states results in a more abrupt modification of the units belonging to the core and is only loosely linked to transitions between global oscillatory states. Third, we characterize different styles of temporal connectivity that cells can exhibit within each state of the sharing network. While inhibitory cells tend to be central, we show that, otherwise, anatomical localization only poorly influences the patterns of temporal connectivity of the different cells. Furthermore, cells can change temporal connectivity style when the network changes state. Altogether, these findings reveal that the sharing of information mediated by the intrinsic dynamics of hippocampal and enthorinal cortex cell assemblies have a rich spatiotemporal structure, which could not have been identified by more conventional time- or state-averaged analyses of functional connectivity.AUTHOR SUMMARYIt is generally thought that computations performed by local brain circuits rely on complex neural processes, associated to the flexible waxing and waning of cell assemblies, i.e. ensemble of cells firing in tight synchrony. Although cell assembly formation is inherently and unavoidably dynamical, it is still common to find studies in which essentially “static” approaches are used to characterize this process. In the present study, we adopt instead a temporal network approach. Avoiding usual time averaging procedures, we reveal that hub neurons are not hardwired but that cells vary smoothly their degree of integration within the assembly core. Furthermore, our temporal network framework enables the definition of alternative possible styles of “hubness”. Some cells may share information with a multitude of other units but only in an intermittent manner, as “activists” in a flash mob. In contrast, some other cells may share information in a steadier manner, as resolute “lobbyists”. Finally, by avoiding averages over pre-imposed states, we show that within each global oscillatory state a rich switching dynamics can take place between a repertoire of many available network states. We thus show that the temporal network framework provides a natural and effective language to rigorously describe the rich spatiotemporal patterns of information sharing instantiated by cell assembly evolution.

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Mining (maximal) Span-cores from Temporal Networks

Cited by 43 publications

References 46 publications

The core decomposition of networks: theory, algorithms and applications

The core decomposition of networks: theory, algorithms and applications

Relevance of temporal cores for epidemic spread in temporal networks

Dynamic core periphery structure of information sharing networks in entorhinal cortex and hippocampus

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