Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which measures the tendency of nodes with the same attribute values to be interconnected. The assortativity coefficient is the Pearson's correlation coefficient of node attribute values across network edges and ranges between -1 and 1. We focus here on the assortativity of binary node attributes and show that properties of the network, such as degree distribution and the number of nodes with each attribute value place constraints upon the attainable values of the assortativity coefficient. We explore the assortativity in three different spaces, that is, ensembles of graph configurations and node-attribute assignments that are valid for a given set of network constraints. We provide means for obtaining bounds on the extremal values of assortativity for each of these spaces. Finally, we demonstrate that under certain conditions the network constraints severely limit the maximum and minimum values of assortativity, which may present issues in how we interpret the assortativity coefficient.Comment: 18 pages, 7 figure

Evaluating risks-based communities of Mafia companies: a complex networks perspective

This paper presents a data-driven complex network approach, to show similarities and differences-in terms of financial risks-between the companies involved in organized crime businesses and those who are not. At this aim, we construct and explore two networks under the assumption that highly connected companies hold similar financial risk profiles of large entity. Companies risk profiles are captured by a statistically consistent overall risk indicator, which is obtained by suitably aggregating four financial risk ratios. The community structures of the networks are analyzed under a statistical perspective, by implementing a rank-size analysis and by investigating the features of their distributions through entropic comparisons. The theoretical model is empirically validated through a high quality dataset of Italian companies. Results highlights remarkable differences between the considered sets of companies, with a higher heterogeneity and a general higher risk profiles in companies traceable back to a crime organization environment

Total variation based community detection using a nonlinear optimization approach

Maximizing the modularity of a network is a successful tool to identify an important community of nodes. However, this combinatorial optimization problem is known to be NP-complete. Inspired by recent nonlinear modularity eigenvector approaches, we introduce the modularity total variation $TV_Q$ and show that its box-constrained global maximum coincides with the maximum of the original discrete modularity function. Thus we describe a new nonlinear optimization approach to solve the equivalent problem leading to a community detection strategy based on $TV_Q$. The proposed approach relies on the use of a fast first-order method that embeds a tailored active-set strategy. We report extensive numerical comparisons with standard matrix-based approaches and the Generalized RatioDCA approach for nonlinear modularity eigenvectors, showing that our new method compares favourably with state-of-the-art alternatives

The Structure of U.S. College Networks on Facebook

Anecdotally, social connections made in university have life-long impact. Yet knowledge of social networks formed in college remains episodic, due in large part to the difficulty and expense involved in collecting a suitable dataset for comprehensive analysis. To advance and systematize insight into college social networks, we describe a dataset of the largest online social network platform used by college students in the United States. We combine de-identified and aggregated Facebook data with College Scorecard data, campus-level information provided by U.S. Department of Education, to produce a dataset covering the 2008-2015 entry year cohorts for 1,159 U.S. colleges and universities, spanning 7.6 million students. To perform the difficult task of comparing these networks of different sizes we develop a new methodology. We compute features over sampled ego-graphs, train binary classifiers for every pair of graphs, and operationalize distance between graphs as predictive accuracy. Social networks of different year cohorts at the same school are structurally more similar to one another than to cohorts at other schools. Networks from similar schools have similar structures, with the public/private and graduation rate dimensions being the most distinguishable. We also relate school types to specific outcomes. For example, students at private schools have larger networks that are more clustered and with higher homophily by year. Our findings may help illuminate the role that colleges play in shaping social networks which partly persist throughout people's lives.Comment: ICWSM-202

Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which aims to quantify the tendency of nodes with the same attribute values to be connected. The assortativity coefficient can be considered as the Pearson’s correlation coefficient of node metadata values across network edges and lies in the interval [−1, 1]. However, properties of the network, such as degree distribution and the distribution of node metadata values place constraints upon the attainable values of the assortativity coefficient. This is important as a particular value of assortativity may say as much about the network topology as about how the metadata are distributed over the network – a fact often overlooked in literature where the interpretation tends to focus simply on the propensity of similar nodes to link to each other, without any regard on the constraints posed by the topology. In this paper we quantify the effect that the topology has on the assortativity coefficient in the case of binary node metadata. Specifically we look at the effect that the degree distribution, or the full topology, and the proportion of each metadata value has on the extremal values of the assortativity coefficient. We provide the means for obtaining bounds on the extremal values of assortativity for different settings and demonstrate that under certain conditions the maximum and minimum values of assortativity are severely limited, which may present issues in interpretation when these bounds are not considered

Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which aims to quantify the tendency of nodes with the same attribute values to be connected. The assortativity coefficient can be considered as the Pearson's correlation coefficient of node metadata values across network edges and lies in the interval [-1,1]. However, properties of the network, such as degree distribution and the distribution of node metadata values, place constraints upon the attainable values of the assortativity coefficient. This is important as a particular value of assortativity may say as much about the network topology as about how the metadata are distributed over the network-a fact often overlooked in literature where the interpretation tends to focus simply on the propensity of similar nodes to link to each other, without any regard on the constraints posed by the topology. In this paper we quantify the effect that the topology has on the assortativity coefficient in the case of binary node metadata. Specifically, we look at the effect that the degree distribution, or the full topology, and the proportion of each metadata value has on the extremal values of the assortativity coefficient. We provide the means for obtaining bounds on the extremal values of assortativity for different settings and demonstrate that under certain conditions the maximum and minimum values of assortativity are severely limited, which may present issues in interpretation when these bounds are not considered