Efficiently inferring community structure in bipartite networks

Structure and inference in annotated networks

For many networks of scientific interest we know both the connections of the network and information about the network nodes, such as the age or gender of individuals in a social network. Here we demonstrate how this 'metadata' can be used to improve our understanding of network structure. We focus in particular on the problem of community detection in networks and develop a mathematically principled approach that combines a network and its metadata to detect communities more accurately than can be done with either alone. Crucially, the method does not assume that the metadata are correlated with the communities we are trying to find. Instead, the method learns whether a correlation exists and correctly uses or ignores the metadata depending on whether they contain useful information. We demonstrate our method on synthetic networks with known structure and on real-world networks, large and small, drawn from social, biological and technological domains.

Efficient community detection of network flows for varying Markov times and bipartite networks

Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest in small-scale structures, shorter timescales may be better. However, current methods for analyzing networks at different timescales require expensive and often infeasible network reconstructions. To overcome this problem, we introduce a method that takes advantage of the inner workings of the map equation and evades the reconstruction step. This makes it possible to efficiently analyze large networks at different Markov times with no extra overhead cost. The method also evades the costly unipartite projection for identifying flow modules in bipartite networks.

Matching-centrality decomposition and the forecasting of new links in networks

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and centrality components provides a comprehensive and unifying quantification of their architecture. The matching term quantifies the assortative structure in which node makes links with which other node, whereas the centrality term quantifies the number of links that nodes make. We show, for a diverse set of networks, that this decomposition can provide a tight fit to observed networks. Then we provide three applications. First, we show that the model allows very accurate prediction of missing links in partially known networks. Second, when node characteristics are known, we show how the matching-centrality decomposition can be related to this external information. Consequently, it offers us a simple and versatile tool to explore how node characteristics explain network architecture. Finally, we demonstrate the efficiency and flexibility of the model to forecast the links that a novel node would create if it were to join an existing network.

Neural Network Spectral Robustness under Perturbations of the Underlying Graph

Recent studies have been using graph-theoretical approaches to model complex networks (such as social, infrastructural, or biological networks) and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how configuration reflects on the coupled behavior in a system of dynamic nodes can be of great importance, for example, in the context of how the brain connectome is affecting brain function. However, the effect of connectivity patterns on network dynamics is far from being fully understood. We study the connections between edge configuration and dynamics in a simple oriented network composed of two interconnected cliques (representative of brain feedback regulatory circuitry). In this article our main goal is to study the spectra of the graph adjacency and Laplacian matrices, with a focus on three aspects in particular: (1) the sensitivity and robustness of the spectrum in response to varying the intra- and intermodular edge density, (2) the effects on the spectrum of perturbing the edge configuration while keeping the densities fixed, and (3) the effects of increasing the network size. We study some tractable aspects analytically, then simulate more general results numerically, thus aiming to motivate and explain our further work on the effect of these patterns on the network temporal dynamics and phase transitions. We discuss the implications of such results to modeling brain connectomics. We suggest potential applications to understanding synaptic restructuring in learning networks and the effects of network configuration on function of regulatory neural circuits.

Ape parasite origins of human malaria virulence genes

Antigens encoded by the var gene family are major virulence factors of the human malaria parasite Plasmodium falciparum, exhibiting enormous intra- and interstrain diversity. Here we use network analysis to show that var architecture and mosaicism are conserved at multiple levels across the Laverania subgenus, based on var-like sequences from eight single-species and three multi-species Plasmodium infections of wild-living or sanctuary African apes. Using select whole-genome amplification, we also find evidence of multi-domain var structure and synteny in Plasmodium gaboni, one of the ape Laverania species most distantly related to P. falciparum, as well as a new class of Duffy-binding-like domains. These findings indicate that the modular genetic architecture and sequence diversity underlying var-mediated host-parasite interactions evolved before the radiation of the Laverania subgenus, long before the emergence of P. falciparum.

Antigens encoded by var genes are major virulence factors of the human malaria parasite Plasmodium falciparum. Here, Larremore et al. identify var-like genes in distantly related Plasmodium species infecting African apes, indicating that these genes already existed in an ancestral ape parasite many millions of years ago.

A unified data representation theory for network visualization, ordering and coarse-graining

Representation of large data sets became a key question of many scientific disciplines in the last decade. Several approaches for network visualization, data ordering and coarse-graining accomplished this goal. However, there was no underlying theoretical framework linking these problems. Here we show an elegant, information theoretic data representation approach as a unified solution of network visualization, data ordering and coarse-graining. The optimal representation is the hardest to distinguish from the original data matrix, measured by the relative entropy. The representation of network nodes as probability distributions provides an efficient visualization method and, in one dimension, an ordering of network nodes and edges. Coarse-grained representations of the input network enable both efficient data compression and hierarchical visualization to achieve high quality representations of larger data sets. Our unified data representation theory will help the analysis of extensive data sets, by revealing the large-scale structure of complex networks in a comprehensible form.

Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors

Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

Bank-firm credit network in Japan: an analysis of a bipartite network

We investigate the networked nature of the Japanese credit market. Our investigation is performed with tools of network science. In our investigation we perform community detection with an algorithm which is identifying communities composed of both banks and firms. We show that the communities obtained by directly working on the bipartite network carry information about the networked nature of the Japanese credit market. Our analysis is performed for each calendar year during the time period from 1980 to 2011. To investigate the time evolution of the networked structure of the credit market we introduce a new statistical method to track the time evolution of detected communities. We then characterize the time evolution of communities by detecting for each time evolving set of communities the over-expression of attributes of firms and banks. Specifically, we consider as attributes the economic sector and the geographical location of firms and the type of banks. In our 32-year-long analysis we detect a persistence of the over-expression of attributes of communities of banks and firms together with a slow dynamic of changes from some specific attributes to new ones. Our empirical observations show that the credit market in Japan is a networked market where the type of banks, geographical location of firms and banks, and economic sector of the firm play a role in shaping the credit relationships between banks and firms.

Cluster analysis of weighted bipartite networks: a new copula-based approach

In this work we are interested in identifying clusters of “positional equivalent” actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We validate it with simulations and applications to real-world data.