Random intersection graphs with communities

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of communities and individuals, where these communities may overlap. We generalize the model, allowing for arbitrary community structures within the communities. In our new model, communities may overlap, and they have their own internal structure described by arbitrary finite community graphs. Our model turns out to be tractable. We analyze the overlapping structure of the communities, show local weak convergence (including convergence of subgraph counts), and derive the asymptotic degree distribution and the local clustering coefficient.

The Complexity of Associative Diffusion: Reassessing the Relationship between Network Structure and Cultural Variation

Goldberg and Stein (2018) present an innovative agent-based computational model that shows how cultural associations can diffuse through superficial interpersonal interactions. They counterintuitively argue that segmented networks—for example, those resembling “small worlds” with dense local clustering—inhibit rather than promote cultural diffusion. This finding is notable because it breaks with a long line of influential research showing that local clustering is crucial to diffusion in cases where behaviors and practices—including cultural beliefs—require multiple reinforcements in order to spread. Replicating Goldberg and Stein’s model, we find this result only holds consistently in settings approximating small-group interactions. In models with larger populations, and where cultural associations require repeated reinforcement through social observation, locally clustered small-world networks can promote global cultural variation as well as globally-connected networks, and sometimes do so better. The complex interactions among parameters that lead to this reversal in Goldberg and Stein’s model are instructive for theoretical models of interpersonal influence.

Structure and Evolution of the International Pesticide Trade Networks

To meet the increasing demand for food around the world, pesticides are widely used and will continue to be widely used in agricultural production to reduce yield losses and maintain product quality. International pesticide trade serves to reallocate the distribution of pesticides around the world. We investigate the statistical properties of the international trade networks of five categories of pesticides from the view angle of temporal directed and weighted networks. We observed an overall increasing trend in network size, network density, average in- and out-degrees, average in- and out-strengths, temporal similarity, and link reciprocity, indicating that the rising globalization of pesticides trade is driving the networks denser. However, the distributions of link weights remain unchanged along time for the five categories of pesticides. In addition, all the networks are disassortatively mixed because large importers or exporters are more likely to trade with small exporters or importers. We also observed positive correlations between in-degree and out-degree, in-strength and out-strength, link reciprocity and in-degree, out-degree, in-strength, and out-strength, while node’s local clustering coefficient is negatively related to in-degree, out-degree, in-strength, and out-strength. We show that some structural and dynamic properties of the international pesticide trade networks are different from those of the international trade networks, highlighting the presence of idiosyncratic features of different goods and products in the international trade.

Identifying Ransomware Actors in the Bitcoin Network

Due to the pseudo-anonymity of the Bitcoin network, users can hide behind their bitcoin addresses that can be generated in unlimited quantity, on the fly, without any formal links between them. Thus, it is being used for payment transfer by the actors involved in ransomware and other illegal activities. The other activity we consider is related to gambling since gambling is often used for transferring illegal funds. The question addressed here is that given temporally limited graphs of Bitcoin transactions, to what extent can one identify common patterns associated with these fraudulent activities and apply themto find other ransomware actors. The problem is rather complex, given that thousands of addresses can belong to the same actor without any obvious links between them and any common pattern of behavior. The main contribution of this paper is to introduce and apply new algorithms for local clustering and supervised graph machine learning for identifying malicious actors. We show that very local subgraphsof the known such actors are sufficient to differentiate between ransomware, random and gambling actors with 85%prediction accuracy on the test data set.

Local clustering via approximate heat kernel PageRank with subgraph sampling

Graph clustering, a fundamental technique in network science for understanding structures in complex systems, presents inherent problems. Though studied extensively in the literature, graph clustering in large systems remains particularly challenging because massive graphs incur a prohibitively large computational load. The heat kernel PageRank provides a quantitative ranking of nodes, and a local cluster can be efficiently found by performing a sweep over the heat kernel PageRank vector. But computing an exact heat kernel PageRank vector may be expensive, and approximate algorithms are often used instead. Most approximate algorithms compute the heat kernel PageRank vector on the whole graph, and thus are dependent on global structures. In this paper, we present an algorithm for approximating the heat kernel PageRank on a local subgraph. Moreover, we show that the number of computations required by the proposed algorithm is sublinear in terms of the expected size of the local cluster of interest, and that it provides a good approximation of the heat kernel PageRank, with approximation errors bounded by a probabilistic guarantee. Numerical experiments verify that the local clustering algorithm using our approximate heat kernel PageRank achieves state-of-the-art performance.

Overlapping Structures Detection in Protein-Protein Interaction Networks Using Community Detection Algorithm Based on Neighbor Clustering Coefficient

With the rapid development of bioinformatics, researchers have applied community detection algorithms to detect functional modules in protein-protein interaction (PPI) networks that can predict the function of unknown proteins at the molecular level and further reveal the regularity of cell activity. Clusters in a PPI network may overlap where a protein is involved in multiple functional modules. To identify overlapping structures in protein functional modules, this paper proposes a novel overlapping community detection algorithm based on the neighboring local clustering coefficient (NLC). The contributions of the NLC algorithm are threefold: (i) Combine the edge-based community detection method with local expansion in seed selection and the local clustering coefficient of neighboring nodes to improve the accuracy of seed selection; (ii) A method of measuring the distance between edges is improved to make the result of community division more accurate; (iii) A community optimization strategy for the excessive overlapping nodes makes the overlapping structure more reasonable. The experimental results on standard networks, Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks and PPI networks show that the NLC algorithm can improve the Extended modularity (EQ) value and Normalized Mutual Information (NMI) value of the community division, which verifies that the algorithm can not only detect reasonable communities but also identify overlapping structures in networks.

Modelling Negative Correlation in Complex Networks Via Anti-Transitivity

Negative correlation appears often in complex networks. For example, in social networks, negative correlation corresponds to rivalry between agents in the network, while in stock market graphs, negative correlation corresponds stocks that move in opposite directions in price action. We present a simplified, deterministic model of negative correlation in networks based on the principle of anti-transitivity: a non-friend of a non-friend is a friend. In the Iterated Local Anti-Transitivity (ILAT) model, for every node u in a given time-step, we add an anti-clone node that is adjacent to the complement of the closed neighborhood of u. We prove that graphs generated by the ILAT model satisfy several properties observed in complex networks, such as high density and densification power laws, constant diameter, and high local clustering. We also prove that the domination and cop numbers of graphs generated by the ILAT model are bounded above by small, absolute constants as time increases.