Four Degrees of Separation, Really

We recently measured the average distance of users in the Facebook graph, spurring comments in the scientific community as well as in the general press ("Four Degrees of Separation"). A number of interesting criticisms have been made about the meaningfulness, methods and consequences of the experiment we performed. In this paper we want to discuss some methodological aspects that we deem important to underline in the form of answers to the questions we have read in newspapers, magazines, blogs, or heard from colleagues. We indulge in some reflections on the actual meaning of "average distance" and make a number of side observations showing that, yes, 3.74 "degrees of separation" are really few

A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.Comment: PASC '18, Code: https://github.com/ligmg/ligm

Using adjacency matrices to lay out larger small-world networks

Many networks exhibit small-world properties. The structure of a small-world network is characterized by short average path lengths and high clustering coefficients. Few graph layout methods capture this structure well which limits their effectiveness and the utility of the visualization itself. Here we present an extension to our novel graphTPP layout method for laying out small-world networks using only their topological properties rather than their node attributes. The Watts–Strogatz model is used to generate a variety of graphs with a small-world network structure. Community detection algorithms are used to generate six different clusterings of the data. These clusterings, the adjacency matrix and edgelist are loaded into graphTPP and, through user interaction combined with linear projections of the adjacency matrix, graphTPP is able to produce a layout which visually separates these clusters. These layouts are compared to the layouts of two force-based techniques. graphTPP is able to clearly separate each of the communities into a spatially distinct area and the edge relationships between the clusters show the strength of their relationship. As a secondary contribution, an edge-grouping algorithm for graphTPP is demonstrated as a means to reduce visual clutter in the layout and reinforce the display of the strength of the relationship between two communities

Linking the network centrality measures closeness and degree

We propose a non-linear relationship between two of the most important measures of centrality in a network: degree and closeness. Based on a shortest-path tree approximation, we give an analytic derivation that shows the inverse of closeness is linearly dependent on the logarithm of degree. We show that our hypothesis works well for a range of networks produced from stochastic network models including the Erdos-Reyni and Barabasi-Albert models. We then test our relation on networks derived from a wide range of real-world data including social networks, communication networks, citation networks, co-author networks, and hyperlink networks. We find our relationship holds true within a few percent in most, but not all, cases. We suggest some ways that this relationship can be used to enhance network analysis

Yi-Er-San topics in network science: centrality, bicycle, triplet

Network science studies interactions between different entities. This thesis covers three different topics in network science: higher-order network structures, human mobility and network centralities. Higher-order network is an emerging field in recent years and combinatorial models use multi-body interactions to describe the structures beyond pairwise. In chapter two, I focus on studying the evolution of the links in temporal networks using three nodes motif-- triplets. In specific, I develop a method that use a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world network data to a model based on pairwise interactions only. The differences between the transition matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test my approach, I used the transition matrix to design a link prediction method-- Triplet Transition score. I investigate the performance of the methods on four temporal networks, comparing my approach against ten other link prediction methods. My results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as I find Triplet Transaction method, along with two other methods based on non-local interactions, gives the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems. In chapter three, I investigate the behaviours of human mobility in different cities using gravity models. Due to previous technical challenges in collecting data on riding behaviours, there have been only a few studies focusing on patterns and regularities of biking traffic. To extend the research, I use the data from mobike and apply the gravity model to study the mobility of dockless bicycles. I validate the effectiveness of the general gravity model on predicting biking traffic at fine spatial resolutions of locations. I then further study the impacts of spatial scale on the gravity model and reveal that the distance-related parameter grows in a similar way as population-related parameters when the spatial scale of locations increases. The result reveals the emergence of the scaling can be explained by the gravity models. Measuring the importance of nodes in networks via centrality measures is an important task in many network systems. There are many centrality measures available and it is speculated that many encode similar information but the reason behind them is rarely studied. In chapter four, I give an explicit non-linear relationship between two of the most popular measures of node centrality: degree and closeness. Based on a shortest-path tree approximation, I give an analytic derivation that shows the inverse of closeness is linearly dependent on the logarithm of degree. I show that the hypothesis works well for a range of networks produced from stochastic network models and for networks derived from many real-world data sets. I connect our results with previous results for other network distance scales such as average distance. My results imply that measuring closeness is broadly redundant unless our relationship is used to remove the dependence on degree from closeness. The success of our relationship suggests that most networks can be approximated by shortest-path spanning trees which are all statistically similar two or more steps away from their root nodes.Open Acces

Disrupting networks of hate: Characterising hateful networks and removing critical nodes

Hateful individuals and groups have increasingly been using the Internet to express their ideas, spread their beliefs, and recruit new members. Under- standing the network characteristics of these hateful groups could help understand individuals’ exposure to hate and derive intervention strategies to mitigate the dangers of such networks by disrupting communications. This article analyses two hateful followers net- works and three hateful retweet networks of Twitter users who post content subsequently classified by hu- man annotators as containing hateful content. Our analysis shows similar connectivity characteristics between the hateful followers networks and likewise between the hateful retweet networks. The study shows that the hateful networks exhibit higher connectivity characteristics when compared to other ”risky” networks, which can be seen as a risk in terms of the likelihood of expo- sure to, and propagation of, online hate. Three network performance metrics are used to quantify the hateful content exposure and contagion: giant component (GC) size, density and average shortest path. In order to efficiently identify nodes whose removal reduced the flow of hate in a network, we propose a range of structured node-removal strategies and test their effectiveness. Results show that removing users with a high degree is most effective in reducing the hateful followers network connectivity (GC, size and density), and therefore reducing the risk of exposure to cyberhate and stemming its propagation

Are collectivistic cultures more prone to rapid transformation? Computational models of cross-cultural differences, social network structure, dynamic social influence, and cultural change

Societies differ in susceptibility to social influence and in the social network structure through which individuals influence each other. What implications might these cultural differences have for changes in cultural norms over time? Using parameters informed by empirical evidence, we computationally modeled these cross-cultural differences to predict two forms of cultural change: consolidation of opinion majorities into stronger majorities, and the spread of initially unpopular beliefs. Results obtained from more than 300,000 computer simulations showed that in populations characterized by greater susceptibility to social influence, there was more rapid consolidation of majority opinion and also more successful spread of initially unpopular beliefs. Initially unpopular beliefs also spread more readily in populations characterized by less densely connected social networks. These computational outputs highlight the value of computational modeling methods as a means to specify hypotheses about specific ways in which cross-cultural differences may have long-term consequences for cultural stability and cultural change

Improving Recommender Systems Using Knowledge Obsolescence as a Predictor of Trust

In the current context of the Social Web, trust has emerged as a concept and mechanism to differentiate users of this Social Web and the content they generate. Much effort has been devoted to study trust predictors with the aim to provide some operational use of the concept. We propose in this work a new predictor for trust: knowledge obsolescence. We provide a characterization of the concept and a description of the relation between trust and knowledge obsolescence. We applied the concept to a generic recommender system. For this purpose, we have developed a software simulator that allow us to test trust and knowledge obsolescence networks in the recommender systems context. Interesting results were obtained. We found that recommender systems success is augmented. Moreover, we found an improvement in some cases for the coverage of potential recommendable items. We did not find statistical significant benefit on the quality of recommendations.Sociedad Argentina de Informática e Investigación Operativa (SADIO

On Improving Distributed Pregel-like Graph Processing Systems

The considerable interest in distributed systems that can execute algorithms to process large graphs has led to the creation of many graph processing systems. However, existing systems suffer from two major issues: (1) poor performance due to frequent global synchronization barriers and limited scalability; and (2) lack of support for graph algorithms that require serializability, the guarantee that parallel executions of an algorithm produce the same results as some serial execution of that algorithm. Many graph processing systems use the bulk synchronous parallel (BSP) model, which allows graph algorithms to be easily implemented and reasoned about. However, BSP suffers from poor performance due to stale messages and frequent global synchronization barriers. While asynchronous models have been proposed to alleviate these overheads, existing systems that implement such models have limited scalability or retain frequent global barriers and do not always support graph mutations or algorithms with multiple computation phases. We propose barrierless asynchronous parallel (BAP), a new computation model that overcomes the limitations of existing asynchronous models by reducing both message staleness and global synchronization while retaining support for graph mutations and algorithms with multiple computation phases. We present GiraphUC, which implements our BAP model in the open source distributed graph processing system Giraph, and evaluate it at scale to demonstrate that BAP provides efficient and transparent asynchronous execution of algorithms that are programmed synchronously. Secondly, very few systems provide serializability, despite the fact that many graph algorithms require it for accuracy, correctness, or termination. To address this deficiency, we provide a complete solution that can be implemented on top of existing graph processing systems to provide serializability. Our solution formalizes the notion of serializability and the conditions under which it can be provided for graph processing systems. We propose a partition-based synchronization technique that enforces these conditions efficiently to provide serializability. We implement this technique into Giraph and GiraphUC to demonstrate that it is configurable, transparent to algorithm developers, and more performant than existing techniques.4 month