Finding Minimum Vertex Covering in Stochastic Graphs: A Learning Automata Approach

Structural and behavioral parameters of many real networks such as social networks are unpredictable, uncertain, and have time-varying parameters, and for these reasons, deterministic graphs for modeling such networks are too restrictive to solve most of the real-network problems. It seems that stochastic graphs, in which weights associated to the vertices are random variables, might be better graph models for real-world networks. Once we use a stochastic graph as the model for a network, every feature of the graph such as path, spanning tree, clique, dominating set, and cover set should be treated as a stochastic feature. For example, choosing a stochastic graph as a graph model of an online social network and defining community structure in terms of clique, the concept of a stochastic clique may be used to study community structures’ properties or define spreading of influence according to the coverage of influential users; the concept of stochastic vertex covering may be used to study spread of influence. In this article, minimum vertex covering in stochastic graphs is first defined, and then four learning, automata-based algorithms are proposed for solving a minimum vertex-covering problem in stochastic graphs where the probability distribution functions of the weights associated with the vertices of the graph are unknown. It is shown that through a proper choice of the parameters of the proposed algorithms, one can make the probability of finding minimum vertex cover in a stochastic graph as close to unity as possible. Experimental results on synthetic stochastic graphs reveal that at a certain confidence level the proposed algorithms significantly outperform the standard sampling method in terms of the number of samples needed to be taken from the vertices of the stochastic graph.     

A comparison of statistical relational learning and graph neural networks for aggregate graph queries

Statistical relational learning (SRL) and graph neural networks (GNNs) are two powerful approaches for learning and inference over graphs. Typically, they are evaluated in terms of simple metrics such as accuracy over individual node labels. Complex aggregate graph queries (AGQ) involving multiple nodes, edges, and labels are common in the graph mining community and are used to estimate important network properties such as social cohesion and influence. While graph mining algorithms support AGQs, they typically do not take into account uncertainty, or when they do, make simplifying assumptions and do not build full probabilistic models. In this paper, we examine the performance of SRL and GNNs on AGQs over graphs with partially observed node labels. We show that, not surprisingly, inferring the unobserved node labels as a first step and then evaluating the queries on the fully observed graph can lead to sub-optimal estimates, and that a better approach is to compute these queries as an expectation under the joint distribution. We propose a sampling framework to tractably compute the expected values of AGQs. Motivated by the analysis of subgroup cohesion in social networks, we propose a suite of AGQs that estimate the community structure in graphs. In our empirical evaluation, we show that by estimating these queries as an expectation, SRL-based approaches yield up to a 50-fold reduction in average error when compared to existing GNN-based approaches.

     

语义增强的大规模多元图简化可视分析方法

网络图可视化可以有效展示网络节点之间的连接关系,广泛应用于诸多领域,如社交网络、知识图谱、生物基因网络等.随着网络数据规模的不断增加,如何简化表达大规模网络图结构已成为图可视化领域中的研究热点.经典的网络图简化可视化方法主要包括图采样、边绑定和图聚类等技术,在减少大量点线交叉造成的视觉紊乱的基础上,提高用户对大规模网络结构的探索和认知效率.然而,上述方法主要侧重于网络图中的拓扑结构,却较少考虑和利用多元图节点的多维属性特征,难以有效提取和表达语义信息,从而无法帮助用户理解大规模多元网络的拓扑结构与多维属性之间的内在关联,为大规模多元图的认知和理解带来困难.因此,本文提出一种语义增强的大规模多元图简化可视分析方法,首先在基于模块度的图聚类算法基础上提取出网络图的层次结构;其次通过多维属性信息熵的计算和比较分析,对网络层次结构进行自适应划分,筛选出具有最优属性聚集特征的社团;进而设计交互便捷的多个关联视图来展示社团之间的拓扑结构、层次关系和属性分布,从不同角度帮助用户分析多维属性在社团形成和网络演化中的作用.大量实验结果表明,本文方法能够有效简化大规模多元图的视觉表达,可以快速分析不同应用领域大规模多元图的关联结构与语义构成,具有较强的实用性.     

基于k-频繁子图聚类的二分图匿名方法

针对以二分图形式发布的社会网络隐私泄露问题,提出了一种面向敏感边识别攻击的社会网络二分图匿名方法。在已有k-安全分组的理论基础上,结合二分图的稀疏性和敏感边识别攻击形式,分别提出了正单向、逆单向以及完全（c1,c2）-安全性原则,并在此基础上,形式化地定义了一类抗敏感边识别攻击的社会网络二分图安全匿名问题;同时,还提出了一种基于k-频繁子图聚类的二分图划分算法和一种基于二分图（c1,c2）-安全性的匿名算法来保证发布二分图的安全性。实验结果表明,该算法在与已有方法相当时间开销的前提下,能产生更小的信息损失度,有效地抵制了敏感边识别攻击,实现了二分图的安全发布。     

一种新的高效图聚集算法

图聚集是将一个大规模的图用简洁的并能有效反映原始图的结构和属性信息的小规模图来表示的技术.图聚集在图数据管理、分析和可视化中发挥着重要作用.图聚集方面现有研究结果还很少,也很不系统.其主要不足之处是:1)算法依赖于具体应用;2)算法仅考虑了图的某方面信息,如结构信息或属性信息;3)算法对用户提供的交互和反馈信息的约束很强.针对现有图聚集算法存在的主要不足,提出一种有向图新型图聚集算法,该算法采用一种新的聚集图质量函数,全面刻画了聚集图多样性、覆盖性、简洁性和实用性.该算法使用LSH(locality sensitive Hashing)技术和基于熵的划分技术,保证了聚集图的质量.在真实数据集上进行了大量的实验,验证了算法的有效性.     

Finding overlapping communities in a complex network of social linkages and Internet of things

Online social networks play an important role in today’s Internet. These social networks contain huge amounts of data and the integrated framework of SN with Internet of things (IoT) presents a challenging problem. IoT is the ubiquitous interconnection of everyday items of interest (things), providing connectivity anytime, anywhere, and with anything. Like biological, co-authorship, and virus-spread networks, IoT and Social Network (SN) can be characterized to be complex networks containing substantial useful information. In the past few years, community detection in graphs has been an active area of research (Lee and Won in Proceedings of IEEE SoutheastCon, pp. 1–5, 2012). Many graph mining algorithms have been proposed, but none of them can help in capturing an important dimension of SNs, which is friendship. A friend circle expands with the help of mutual friends, and, thus, mutual friends play an important role in social networks’ growth. We propose two graph clustering algorithms: one for undirected graphs such as Facebook and Google+, and the other for directed graphs such as Twitter. The algorithms extract communities, and based on the access control policy nodes share resources (things). In the proposed Community Detection in Integrated IoT and SN (CDIISN) algorithm, we divide the nodes/actors of complex networks into basic, and IoT nodes. We, then, execute the community detection algorithm on them. We take nodes of a graph as members of a SN, and edges depicting the relations between the nodes. The CDIISN algorithm is purely deterministic, and no fuzzy communities are formed. It is known that one community detection algorithm is not suitable for all types of networks. For different network structures, different algorithms exhibit different results, and methods of execution. However, in our proposed method, the community detection algorithm can be modified as desired by a user based on the network connections. The proposed community detection approach is unique in the sense that a user can define his community detection criteria based on the kind of network.     

Generalized framework for personalized recommendations in agent networks

An agent network can be modeled as a directed weighted graph whose vertices represent agents and edges represent a trust relationship between the agents. This article proposes a new recommendation approach, dubbed LocPat, which can recommend trustworthy agents to a requester in an agent network. We relate the recommendation problem to the graph similarity problem, and define the similarity measurement as a mutually reinforcing relation. We understand an agent as querying an agent network to which it belongs to generate personalized recommendations. We formulate a query into an agent network as a structure graph applied in a personalized manner that reflects the pattern of relationships centered on the requesting agent. We use this pattern as a basis for recommending an agent or object (a vertex in the graph). By calculating the vertex similarity between the agent network and a structure graph, we can produce a recommendation based on similarity scores that reflect both the link structure and the trust values on the edges. Our resulting approach is generic in that it can capture existing network-based approaches merely through the introduction of appropriate structure graphs. We evaluate different structure graphs with respect to two main kinds of settings, namely, social networks and ratings networks. Our experimental results show that our approach provides personalized and flexible recommendations effectively and efficiently based on local information.     

Unfolding Edges: Adding Context to Edges in Multivariate Graph Visualization

Existing work on visualizing multivariate graphs is primarily concerned with representing the attributes of nodes. Even though edges are the constitutive elements of networks, there have been only few attempts to visualize attributes of edges. In this work, we focus on the critical importance of edge attributes for interpreting network visualizations and building trust in the underlying data. We propose ‘unfolding of edges’ as an interactive approach to integrate multivariate edge attributes dynamically into existing node-link diagrams. Unfolding edges is an in-situ approach that gradually transforms basic links into detailed representations of the associated edge attributes. This approach extends focus+context, semantic zoom, and animated transitions for network visualizations to accommodate edge details on-demand without cluttering the overall graph layout. We explore the design space for the unfolding of edges, which covers aspects of making space for the unfolding, of actually representing the edge context, and of navigating between edges. To demonstrate the utility of our approach, we present two case studies in the context of historical network analysis and computational social science. For these, web-based prototypes were implemented based on which we conducted interviews with domain experts. The experts' feedback suggests that the proposed unfolding of edges is a useful tool for exploring rich edge information of multivariate graphs.     

Node and edge selectivity estimation for range queries in spatial networks

Modern applications requiring spatial network processing pose several interesting query optimization challenges. Spatial networks are usually represented as graphs, and therefore, queries involving a spatial network can be executed by using the corresponding graph representation. This means that the cost for executing a query is determined by graph properties such as the graph order and size (i.e., number of nodes and edges) and other graph parameters. In this paper, we present novel methods to estimate the number of nodes and edges in regions of interest in spatial networks, towards predicting the space and time requirements for range queries. The methods are evaluated by using real-life and synthetic data sets. Experimental results show that the number of nodes and edges can be estimated efficiently and accurately, with relatively small space requirements, thus providing useful information to the query optimizer.     

社交网络隐私保护中的随机算法

提出了一种基于高斯随机乘法的社交网络隐私保护方法.该算法利用无向有权图表示社交网络,通过高斯随机乘法来扰乱其边的权重,保持网络最短路径不变并使其长度应与初始网络的路径长度尽可能接近,以实现对社交网络的隐私保护.从理论上证明了算法的可行性及完美算法的不存在性.采用这种随机乘法得到的仿真结果符合理论分析结果.     

UNMAT: Visual comparison and exploration of uncertainty in large graph sampling

Graph sampling, simplying the networks while preserving primary graph characteristics, provides a convenient means for exploring large network. During the last few years a variety of graph sampling algorithms have been proposed, and the evaluation and comparison of the algorithms has witnessed a growing interest. Although different tests have been conducted, an important aspect of graph sampling, namely, uncertainty in graph sampling, has been ignored so far. Additionally, existing studies mainly rely on simple statistical analysis and a few relatively small datasets. They may not be applicable to other more complicated graphs with much larger numbers of nodes and edges. Furthermore, while graph clustering is becoming increasingly important, it is still unknown how different sampling algorithms and their associated uncertainty can impact the subsequent graph analysis, such as graph clustering. In this work, we propose an efficient visual analytics framework for measuring the uncertainty from different graph sampling methods and quantifying the influence of the uncertainty in general graph analysis procedures. A spreadsheet-style visualization with rich user interactions is presented to facilitate visual comparison and analysis of multiple graph sampling algorithms. Our framework helps users gain a better understanding of the graph sampling methods in producing uncertainty information. The framework also makes it possible for users to quickly evaluate graph sampling algorithms and select the most appropriate one for their applications.     

gbase: an efficient analysis platform for large graphs

Graphs appear in numerous applications including cyber security, the Internet, social networks, protein networks, recommendation systems, citation networks, and many more. Graphs with millions or even billions of nodes and edges are common-place. How to store such large graphs efficiently? What are the core operations/queries on those graph? How to answer the graph queries quickly? We propose Gbase, an efficient analysis platform for large graphs. The key novelties lie in (1) our storage and compression scheme for a parallel, distributed settings and (2) the carefully chosen graph operations and their efficient implementations. We designed and implemented an instance of Gbase using Mapreduce/Hadoop. Gbase provides a parallel indexing mechanism for graph operations that both saves storage space, as well as accelerates query responses. We run numerous experiments on real and synthetic graphs, spanning billions of nodes and edges, and we show that our proposed Gbase is indeed fast, scalable, and nimble, with significant savings in space and time.     

BA-GNN: Behavior-aware graph neural network for session-based recommendation

Session-based recommendation is a popular research topic that aims to predict users’ next possible interactive item by exploiting anonymous sessions. The existing studies mainly focus on making predictions by considering users’ single interactive behavior. Some recent efforts have been made to exploit multiple interactive behaviors, but they generally ignore the influences of different interactive behaviors and the noise in interactive sequences. To address these problems, we propose a behavior-aware graph neural network for session-based recommendation. First, different interactive sequences are modeled as directed graphs. Thus, the item representations are learned via graph neural networks. Then, a sparse self-attention module is designed to remove the noise in behavior sequences. Finally, the representations of different behavior sequences are aggregated with the gating mechanism to obtain the session representations. Experimental results on two public datasets show that our proposed method outperforms all competitive baselines. The source code is available at the website of GitHub.     

Structure Indicators for Transportation Graph Analysis I: Planar Connected Simple Graphs

The paper deals with the representation of a transportation infrastructure by a planar connected simple graph and aims at studying its features through the analysis of graph properties. All planar and connected graphs with 4 up to 7 edges are analysed and compared to extract the most suitable parameters to investigate some network features. Then, a set of 41 graphs representing some actual underground networks are also analysed. Besides, as a third scenario, the underground network of Milan, along its development in years, is proposed in order to apply the proposed methodology. Many parameters are taken into consideration. Some of them are already discussed in literature, such as the eigenvalues and gaps of adjacency matrix or such as the “classical” parameters α, β, γ. Others, such as the first two Betti numbers, are new for these applications. In order to overcome the problem of comparing features of graphs with different size, the normalisation of these parameters is considered. Some relationships between Betti numbers, eigenvalues, and classical parameters are also investigated. Results show that the eigenvalues and gaps of the adjacency matrix well represent some features of the graphs while combining them with the Betti numbers, a more significant interpretation can be achieved. Particularly, their normalised values are able to describe the increasing complexity of a graph.     

Adding regular expressions to graph reachability and pattern queries

It is increasingly common to find graphs in which edges are of different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity of a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubic-time algorithms for evaluating graph pattern queries, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. (4) The effectiveness and efficiency of these algorithms are experimentally verified using real-life data and synthetic data.     

社交网络下的不确定图隐私保护算法

社交网络平台的快速普及使得社交网络中的个人隐私泄露问题愈发受到用户的关心,传统的数据隐私保护方法无法满足用户数量巨大、关系复杂的社交网络隐私保护需求.图修改技术是针对社交网络数据的隐私保护所提出的一系列隐私保护措施,其中不确定图是将确定图转化为概率图的一种隐私保护方法.主要研究了不确定图中边概率赋值算法,提出了基于差分隐私的不确定图边概率赋值算法,该算法具有双重隐私保障,适合社交网络隐私保护要求高的场景.同时提出了基于三元闭包的不确定图边概率分配算法,该算法在实现隐私保护的同时保持了较高的数据效用,适合简单的社交网络隐私保护场景.分析与比较表明：与（k,ε）-混淆算法相比,基于差分隐私的不确定图边概率赋值算法可以实现较高的隐私保护效果,基于三元闭包的不确定图边概率分配算法具有较高的数据效用性.最后,为了衡量网络结构的失真程度,提出了基于网络结构熵的数据效用性度量算法,该算法能够度量不确定图与原始图结构的相似程度.     

A calculus for stochastic QoS analysis

The issue of Quality of Service (QoS) performance analysis in packet-switched networks has drawn a lot of attention in the networking community. There is a lot of work including an elegant theory under the name of network calculus, which focuses on analysis of deterministic worst case QoS performance bounds. In the meantime, researchers have studied stochastic QoS performance for specific schedulers. However, most previous works on deterministic QoS analysis or stochastic QoS analysis have only considered a server that provides deterministic service, i.e. deterministically bounded rate service. Few have considered the behavior of a stochastic server that provides input flows with variable rate service, for example wireless links. In this paper, we propose a stochastic network calculus to analyze the end-to-end stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastic servers. We also prove that a server serving an aggregate of flows can be regarded as a stochastic server for individual flows within the aggregate. Based on this, the proposed framework is further applied to analyze per-flow stochastic QoS performance under aggregate scheduling.     

基于边采样的网络表示学习模型

近年来,以微博、微信、Facebook为代表的社交网络不断发展,网络表示学习引起了学术界和工业界的广泛关注。传统的网络表示学习模型利用图矩阵表示的谱特性,由于其效率低下、效果不佳,难以应用到真实网络中。近几年,基于神经网络的表示学习方法因算法效率高、能较好保存网络结构信息,逐渐成为网络表示学习的主流算法。网络中的节点因为不同类型的关系而相互连接,这些关系里隐藏了非常丰富的信息（如兴趣、家人）,但所有现存方法都没有区分节点之间边的关系类型。本文提出一个能够编码这种关系信息的无监督网络表示学习模型NEES,首先通过边采样得到能够反映边关系类型信息的边向量,其次利用边向量为图中每个节点学习到一个低维表示。我们分别在几个真实网络数据上进行了多标签分类、边预测等任务,实验结果表明NEES方法能取得超过现存最好算法的优异效果,且其是可规模化的,可以很好地应用于大型网络的表示与计算。     

A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention it merits. This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable. This becomes more difficult if we assume that the probability distribution function of the edge weight is unknown. In this paper, we propose a learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown. The proposed algorithm taking advantage of learning automata determines the edges that must be sampled at each stage. As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight. The proposed learning automata-based sampling method decreases the number of samples that need to be taken from the graph by reducing the rate of unnecessary samples. Experimental results show the superiority of the proposed algorithm over the well-known existing methods both in terms of the number of samples and the running time of algorithm.     

基于图神经网络的异构信任推荐算法

传统基于图神经网络的社交推荐算法通过加强用户和项目特征的学习提升预测精度,但随着用户数据日益稀疏和社交关系趋于复杂,推荐质量提升缓慢。为挖掘用户和项目的潜在关联关系,提出一种结合图神经网络的异构信任推荐算法（GraphTrust）。在显式信任关系的基础上获取用户的潜在好友,根据动态影响力传播模型将图神经网络中的节点和边进行分类,通过不同类型的边在不同节点间进行影响力传播扩散,捕捉隐藏在高阶网络结构中的影响力扩散特征,并使用户和项目的潜在特征随着影响力传播过程达到平衡状态,最终将用户交互的项目特征作为辅助特征与用户特征聚合进行评分预测。在Yelp和Flickr数据集上的实验结果表明,当潜在特征维数为64时,GraphTrust算法相比于DiffNet++算法的命中率和归一化折损累计增益分别提升了13.2%、22.2%和20.4%、25.5%,在一定程度上提高了推荐过程的可解释性和预测精度,并且缓解了数据稀疏问题。