Cyber Insurance Ratemaking: A Graph Mining Approach

Cyber insurance ratemaking (CIRM) is a procedure used to set rates (or prices) for cyber insurance products provided by insurance companies. Rate estimation is a critical issue for cyber insurance products. This problem arises because of the unavailability of actuarial data and the uncertainty of normative standards of cyber risk. Most cyber risk analyses do not consider the connection between Information Communication and Technology (ICT) sources. Recently, a cyber risk model was developed that considered the network structure. However, the analysis of this model remains limited to an unweighted network. To address this issue, we propose using a graph mining approach (GMA) to CIRM, which can be applied to obtain fair and competitive prices based on weighted network characteristics. This study differs from previous studies in that it adds the GMA to CIRM and uses communication models to explain the frequency of communications as weights in the network. We used the heterogeneous generalized susceptible-infectious-susceptible model to accommodate different infection rates. Our approach adds up to the existing method because it considers the communication frequency and GMA in CIRM. This approach results in heterogeneous premiums. Additionally, GMA can choose more active communications to reflect high communications contribution in the premiums or rates. This contribution is not found when the infection rates are the same. Based on our experimental results, it is apparent that this method can produce more reasonable and competitive prices than other methods. The prices obtained with GMA and communication factors are lower than those obtained without GMA and communication factors.

FONDUE: A Framework for Node Disambiguation and Deduplication Using Network Embeddings

Data often have a relational nature that is most easily expressed in a network form, with its main components consisting of nodes that represent real objects and links that signify the relations between these objects. Modeling networks is useful for many purposes, but the efficacy of downstream tasks is often hampered by data quality issues related to their construction. In many constructed networks, ambiguity may arise when a node corresponds to multiple concepts. Similarly, a single entity can be mistakenly represented by several different nodes. In this paper, we formalize both the node disambiguation (NDA) and node deduplication (NDD) tasks to resolve these data quality issues. We then introduce FONDUE, a framework for utilizing network embedding methods for data-driven disambiguation and deduplication of nodes. Given an undirected and unweighted network, FONDUE-NDA identifies nodes that appear to correspond to multiple entities for subsequent splitting and suggests how to split them (node disambiguation), whereas FONDUE-NDD identifies nodes that appear to correspond to same entity for merging (node deduplication), using only the network topology. From controlled experiments on benchmark networks, we find that FONDUE-NDA is substantially and consistently more accurate with lower computational cost in identifying ambiguous nodes, and that FONDUE-NDD is a competitive alternative for node deduplication, when compared to state-of-the-art alternatives.

The asymptotic formula on average weighted path length for scale-free modular network

In this paper, we discuss the average path length for a class of scale-free modular networks with deterministic growth. To facilitate the analysis, we define the sum of distances from all nodes to the nearest hub nodes and the nearest peripheral nodes. For the unweighted network, we find that whether the scale-free modular network is single-hub or multiple-hub, the average path length grows logarithmically with the increase of nodes number. For the weighted network, we deduce that when the network iteration [Formula: see text] tends to infinity, the average weighted shortest path length is bounded, and the result is independent of the connection method of network.

On the Existence of Pairwise Stable Weighted Networks

In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg’s existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

A new method for Community detection in complex network on the basis of Similarity

Introduction: Regarding complex network, to find optimal communities in the network has become a key topic in the field of network theory. It is crucial to understand the Structure and functionality of associated networks. In this paper, we propose a new method of community detection that works on the structural similarity of a network (SSN). Method: This method works in two steps, at the first step, it removes edges between the different groups of nodes which are not very similar to each other. As a result of edge removal, the network is divided into many small random communities, which are referred as main communities. Result: In the second step, we apply the evaluation method (EM), it chooses the best quality communities, from all main communities which already produced at the first step. At last, we apply evaluation metrics to our proposed method and benchmarking methods, which show that the SSN method can detect comparatively more accurate results than other methods in this paper. Conclusion: In this article, we proposed a novel method for community detection in networks, called structural similarity of network (SSN). It works in two steps. In the first step, it randomly removes low similarity edges from the network, which makes several small disconnected communities, called as main communities. Afterward, the main communities are merged to search for the final communities, which are near to actual existing communities of the network. Discussion: This approach is defined on the base of the unweighted network, so in Further research it could be used on weighted networks and can explore some new deep-down attributes. Furthermore, it will be used Facebook and twitter weighted data with the artificial intelligence approach.

THE AVERAGE WEIGHTED PATH LENGTH FOR A CLASS OF HIERARCHICAL NETWORKS

In this paper, in order to calculate the average path length for unweighted and weighted hierarchical networks, we define the sum of the distances from each node to the vertex and the bottom nodes. For the unweighted network, we show that the average path length grows with the size of [Formula: see text] as [Formula: see text]. For the weighted network, we prove its weighted path length approaches a constant related to the weighting factor [Formula: see text] and parameter [Formula: see text]. In particular, for [Formula: see text], the average weighted path length of the network tends to a specific value [Formula: see text].

Critical Nodes Identification in Complex Networks

Critical nodes identification in complex networks is significance for studying the survivability and robustness of networks. The previous studies on structural hole theory uncovered that structural holes are gaps between a group of indirectly connected nodes and intermediaries that fill the holes and serve as brokers for information exchange. In this paper, we leverage the property of structural hole to design a heuristic algorithm based on local information of the network topology to identify node importance in undirected and unweighted network, whose adjacency matrix is symmetric. In the algorithm, a node with a larger degree and greater number of structural holes associated with it, achieves a higher importance ranking. Six real networks are used as test data. The experimental results show that the proposed method not only has low computational complexity, but also outperforms degree centrality, k-shell method, mapping entropy centrality, the collective influence algorithm, DDN algorithm that based on node degree and their neighbors, and random ranking method in identifying node importance for network connectivity in complex networks.

Context Attention Heterogeneous Network Embedding

Network embedding (NE), which maps nodes into a low-dimensional latent Euclidean space to represent effective features of each node in the network, has obtained considerable attention in recent years. Many popular NE methods, such as DeepWalk, Node2vec, and LINE, are capable of handling homogeneous networks. However, nodes are always fully accompanied by heterogeneous information (e.g., text descriptions, node properties, and hashtags) in the real-world network, which remains a great challenge to jointly project the topological structure and different types of information into the fixed-dimensional embedding space due to heterogeneity. Besides, in the unweighted network, how to quantify the strength of edges (tightness of connections between nodes) accurately is also a difficulty faced by existing methods. To bridge the gap, in this paper, we propose CAHNE (context attention heterogeneous network embedding), a novel network embedding method, to accurately determine the learning result. Specifically, we propose the concept of node importance to measure the strength of edges, which can better preserve the context relations of a node in unweighted networks. Moreover, text information is a widely ubiquitous feature in real-world networks, e.g., online social networks and citation networks. On account of the sophisticated interactions between the network structure and text features of nodes, CAHNE learns context embeddings for nodes by introducing the context node sequence, and the attention mechanism is also integrated into our model to better reflect the impact of context nodes on the current node. To corroborate the efficacy of CAHNE, we apply our method and various baseline methods on several real-world datasets. The experimental results show that CAHNE achieves higher quality compared to a number of state-of-the-art network embedding methods on the tasks of network reconstruction, link prediction, node classification, and visualization.