The work on large-scale graph analytics to date has largely focused on the study of static properties of graph snapshots. However, a static view of interactions between entities is often an oversimplification of several complex phenomena like the spread of epidemics, information diffusion, formation of online communities , and so on. Being able to find temporal interaction patterns, visualize the evolution of graph properties, or even simply compare them across time, adds significant value in reasoning over graphs. However, because of lack of underlying data management support, an analyst today has to manually navigate the added temporal complexity of dealing with large evolving graphs. In this paper, we present a system, called Historical Graph Store, that enables users to store large volumes of historical graph data and to express and run complex temporal graph analytical tasks against that data. It consists of two key components: a Temporal Graph Index (TGI), that compactly stores large volumes of historical graph evolution data in a partitioned and distributed fashion; it provides support for retrieving snapshots of the graph as of any timepoint in the past or evolution histories of individual nodes or neighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for expressing complex temporal analytical tasks and for executing them in an efficient and scalable manner. Our experiments demonstrate our system's efficient storage, retrieval and analytics across a wide variety of queries on large volumes of historical graph data.
Temporal graph analytics is an area of growing interest. Evolution of shortest paths in dynamic graphs has been studies by @cite_21 , @cite_53 , and @cite_26 . Evolution of community structures in graphs has been of interest as well @cite_18 @cite_3 @cite_28 @cite_2 . Change in page rank with evolving graphs @cite_14 @cite_43 , and the study of change in centrality of vertices, path lengths of vertex pairs, etc. @cite_33 , also lie under the larger umbrella of temporal graph analysis. @cite_7 provide a taxonomy of analytical tasks over evolving graphs. @cite_44 , provide a good reference for studying several dynamic processes modeled over graphs. Our system significantly reduces the effort involved in building and deploying such analytics over large volumes of graph data.
@cite_18 @cite_26 @cite_14 @cite_33 @cite_7 @cite_28 @cite_53 @cite_21 @cite_3 @cite_44 @cite_43 @cite_2
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Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths connecting one terminal to the other. Herein, we consider two models of temporal paths: paths that pass through arbitrarily many edges per time step (non-strict) and paths that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NP-hardness versus polynomial-time solvability) for both problem variants. Moreover we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. We further show that, on temporal graphs with planar underlying graph, if additionally the number of time steps is constant, then the problem variant for strict paths is solvable in quasi-linear time. Finally, we introduce and motivate the notion of a temporal core (vertices whose incident edges change over time). We prove that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores. A temporal graph is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence (G_1,G_2 ,G_l ) of static graphs over the same (static) set of nodes V. Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and algorithmic principles. Recent research shows that many graph properties and problems become radically different and usually substantially more difficult when an extra time dimension in added to them. Moreover, there is already a rich and rapidly growing set of modern systems and applications that can be naturally modeled and studied via temporal graphs. This, further motivates the need for the development of a temporal extension of graph theory. We survey here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community. Graph-like data appears in many applications, such as social networks, internet hyperlinks, roadmaps, etc. and in most cases, graphs are dynamic, evolving through time. In this work, we study the problem of efficient shortest-path query evaluation on evolving social graphs. Our shortest-path queries are "temporal": they can refer to any time-point or time-interval in the graph's evolution, and corresponding valid answers should be returned. To efficiently support this type of temporal query, we extend the traditional Dijkstra's algorithm to compute shortest-path distance(s) for a time-point or a time-interval. To speed up query processing, we explore preprocessing index techniques such as Contraction Hierarchies (CH). Moreover, we examine how to maintain the evolving graph along with the index by utilizing temporal partition strategies. Experimental evaluations on real world datasets and large synthetic datasets demonstrate the feasibility and scalability of our proposed efficient techniques and optimizations. 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.