In this paper, we address the problem of evaluating historical queries on graphs. To this end, we investigate the use of graph deltas, i.e., a log of time-annotated graph operations. Our storage model maintains the current graph snapshot and the delta. We reconstruct past snapshots by applying appropriate parts of the graph delta on the current snapshot. Query evaluation proceeds on the reconstructed snapshots but we also propose algorithms based mostly on deltas for efficiency. We introduce various techniques for improving performance, including materializing intermediate snapshots, partial reconstruction and indexing deltas.
There is also a large body of work that studies the evolution of real-world networks over time. In @cite_13 , it was shown that for a variety of real-world networks, graph density increases following a power-low and the graph diameter shrinks. Works on specific networks such as Flickr @cite_8 and Facebook @cite_9 also study network growth and their results can be exploited to enrich our model.
@cite_9 @cite_13 @cite_8
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Social networks are popular platforms for interaction, communication and collaboration between friends. Researchers have recently proposed an emerging class of applications that leverage relationships from social networks to improve security and performance in applications such as email, web browsing and overlay routing. While these applications often cite social network connectivity statistics to support their designs, researchers in psychology and sociology have repeatedly cast doubt on the practice of inferring meaningful relationships from social network connections alone. This leads to the question: Are social links valid indicators of real user interaction? If not, then how can we quantify these factors to form a more accurate model for evaluating socially-enhanced applications? In this paper, we address this question through a detailed study of user interactions in the Facebook social network. We propose the use of interaction graphs to impart meaning to online social links by quantifying user interactions. We analyze interaction graphs derived from Facebook user traces and show that they exhibit significantly lower levels of the "small-world" properties shown in their social graph counterparts. This means that these graphs have fewer "supernodes" with extremely high degree, and overall network diameter increases significantly as a result. To quantify the impact of our observations, we use both types of graphs to validate two well-known social-based applications (RE and SybilGuard). The results reveal new insights into both systems, and confirm our hypothesis that studies of social applications should use real indicators of user interactions in lieu of social graphs. How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. How do real graphs evolve over timeq What are normal growth patterns in social, technological, and information networksq Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)). Existing graph generation models do not exhibit these types of behavior even at a qualitative level. We provide a new graph generator, based on a forest fire spreading process that has a simple, intuitive justification, requires very few parameters (like the flammability of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. We also notice that the forest fire model exhibits a sharp transition between sparse graphs and graphs that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks exhibit this type of relation between densification and the degree distribution. The rapid growth in the volume of many real-world graphs (e.g., social networks, web graphs, and spatial networks) has led to the development of various vertex-centric distributed graph computing systems in recent years. However, real-world graphs from different domains have very different characteristics, which often create bottlenecks in vertex-centric parallel graph computation. We identify three such important characteristics from a wide spectrum of real-world graphs, namely (1)skewed degree distribution, (2)large diameter, and (3)(relatively) high density. Among them, only (1) has been studied by existing systems, but many real-world power-law graphs also exhibit the characteristics of (2) and (3). In this paper, we propose a block-centric framework, called Blogel, which naturally handles all the three adverse graph characteristics. Blogel programmers may think like a block and develop efficient algorithms for various graph problems. We propose parallel algorithms to partition an arbitrary graph into blocks efficiently, and block-centric programs are then run over these blocks. Our experiments on large real-world graphs verified that Blogel is able to achieve orders of magnitude performance improvements over the state-of-the-art distributed graph computing systems.