Many real-world networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (which represent people in the case of social networks) are represented by time-stamped edges. One of the most fundamental problems in (social) network analysis is community detection, and one of the most basic primitives to model a community is a clique. Addressing the problem of finding communities in temporal networks, [TCS 2016] introduced @math -cliques as a natural temporal version of cliques. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm to enumerate @math -cliques. We continue this work and improve and extend the algorithm of to enumerate temporal @math -plexes (notably, cliques are the special case @math ). We define a @math - @math -plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive @math time steps at least one edge to all but at most @math vertices in the chosen set of vertices. We develop a recursive algorithm for enumerating all maximal @math - @math -plexs and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach. In particular, for the special case of @math -1-plexes (that is, @math -cliques), we observe that our algorithm is on average significantly faster than the previous algorithms by [SNAM 2017] and [IPL 2018] for enumerating @math -cliques.
Aside from community detection, many other problem areas also have been studied in the context of temporal graphs, including connectivity problems @cite_21 @cite_18 @cite_42 @cite_16 @cite_17 , graph exploration @cite_20 @cite_32 , clustering @cite_40 , and covering problems @cite_22 @cite_8 . For an extended overview on research related to temporal graphs, we refer to the surveys of Holme and Saram "aki @cite_33 , Casteigts and Flocchini @cite_1 @cite_15 , Michail @cite_29 , and @cite_30 .
@cite_30 @cite_18 @cite_22 @cite_33 @cite_8 @cite_29 @cite_21 @cite_42 @cite_32 @cite_1 @cite_40 @cite_15 @cite_16 @cite_20 @cite_17
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Time-wise knowledge is relevant in knowledge graphs as the majority facts are true in some time period, for instance, (Barack Obama, president of, USA, 2009, 2017). Consequently, temporal information extraction and temporal scoping of facts in knowledge graphs have been a focus of recent research. Due to this, a number of temporal knowledge graphs have become available such as YAGO and Wikidata. In addition, since the temporal facts are obtained from open text, they can be weighted, i.e., the extraction tools assign each fact with a confidence score indicating how likely that fact is to be true. Temporal facts coupled with confidence scores result in a probabilistic temporal knowledge graph. In such a graph, probabilistic query evaluation (marginal inference) and computing most probable explanations (MPE inference) are fundamental problems. In addition, in these problems temporal coalescing, an important research in temporal databases, is very challenging. In this work, we study these problems by using probabilistic programming. We report experimental results comparing the efficiency of several state of the art systems. Abstract We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding Temporal ( s , z ) -Separation problem is NP -complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph—there we observe polynomial-time solvability in the case of bounded treewidth—as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases. Given a set of plausible detections, detected at each time instant independently, we investigate how to associate them across time. This is done by propagating labels on a set of graphs that capture how the spatio-temporal and the appearance cues promote the assignment of identical or distinct labels to a pair of nodes. The graph construction is driven by the locally linear embedding (LLE) of either the spatio-temporal or the appearance features associated to the detections. Interestingly, the neighborhood of a node in each appearance graph is defined to include all nodes for which the appearance feature is available (except the ones that coexist at the same time). This allows to connect the nodes that share the same appearance even if they are temporally distant, which gives our framework the uncommon ability to exploit the appearance features that are available only sporadically along the sequence of detections. Once the graphs have been defined, the multi-object tracking is formulated as the problem of finding a label assignment that is consistent with the constraints captured by each of the graphs. This results into a difference of convex program that can be efficiently solved. Experiments are performed on a basketball and several well-known pedestrian datasets in order to validate the effectiveness of the proposed solution. This paper presents our work in mapping the design space of techniques for temporal graph visualisation. We identify two independent dimensions upon which the techniques can be classified: graph structural encoding and temporal encoding. Based on these dimensions, we create a matrix into which we organise existing techniques. We identify gaps in this design space which may prove interesting opportunities for the development of novel techniques. We also consider additional dimensions on which further useful classification could be made. In organising the disparate existing approaches from a wide range of domains, our classification will assist those new to the research area, and designers and evaluators developing systems for temporal graph data by raising awareness of the range of possible approaches available, and highlighting possible directions for further research.