Directionality of real world networks as predicted by path length in directed and undirected graphs

Rosen, Yonatan; Louzoun, Yoram

doi:10.1016/j.physa.2014.01.005

Cited by 11 publications

(4 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the problem of directionality is a recurrent topic in connectomics, with few exceptions (Négyessy, Nepusz, Zalányi, & Bazsó, 2008 ; Rosen & Louzoun, 2014 ), most work has focused on identifying the directionality of the interactions from the dynamics of nodes. The directionality of the interactions of nodes in motifs and networks is paramount to shaping the dynamics of systems (Bargmann & Marder, 2013 ).…”

Section: Discussionmentioning

confidence: 99%

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Kale

Zalesky

Gollo

2018

Network Neuroscience

View full text Add to dashboard Cite

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

show abstract

Section: Discussionmentioning

confidence: 99%

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Kale

Zalesky

Gollo

2018

Network Neuroscience

View full text Add to dashboard Cite

show abstract

“…• Flow -a hierarchy measure that approximates topological sorting for graphs with cycles (Rosen and Louzoun [2014]).…”

Section: Algorithm Efficacy -Real World Networkmentioning

confidence: 99%

BFS based distributed algorithm for parallel local directed sub-graph enumeration

Levinas¹,

Roy²,

Louzoun³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Estimating the frequency of sub-graphs is of importance for many tasks, including sub-graph isomorphism, kernel-based anomaly detection, and network structure analysis. While multiple algorithms were proposed for full enumeration or sampling-based estimates, these methods fail in very large graphs. Recent advances in parallelization allow for estimates of total sub-graphs counts in very large graphs. The task of counting the frequency of each sub-graph associated with each vertex also received excellent solutions for undirected graphs. However, there is currently no good solution for very large directed graphs. We here propose VDMC (Vertex specific Distributed Motif Counting) -a fully distributed algorithm to optimally count all the 3 and 4 vertices connected directed graphs (sub-graph motifs) associated with each vertex of a graph. VDMC counts each motif only once and its efficacy is linear in the number of counted motifs. It is fully parallelized to be efficient in GPU-based computation. VDMC is based on three main elements: 1) Ordering the vertices and only counting motifs containing increasing order vertices, 2) sub-ordering motifs based on the average length of the BFS composing the motif, and 3) removing isomorphisms only once for the entire graph. We here compare VDMC to analytical estimates of the expected number of motifs and show its accuracy. VDMC is available as a highly efficient CPU and GPU code with a novel data structure for efficient graph manipulation. We show the efficacy of VDMC and real-world graphs. VDMC allows for the precise analysis of sub-graph frequency around each vertex in large graphs and opens the way for the extension of methods until now limited to graphs of thousands of edges to graphs with millions of edges and above.

show abstract

“…• Flow (Rosen and Louzoun 2014). We define the flow a node as the ratio between the directed and undirected distances between this node and all other nodes.…”

Section: Product Similarity Networkmentioning

confidence: 99%

Topology of products similarity network for market forecasting

et al. 2019

Self Cite

View full text Add to dashboard Cite

The detection and prediction of risk in financial markets is one of the main challenges of economic forecasting, and draws much attention from the scientific community. An even more challenging task is the prediction of the future relative gain of companies. We here develop a novel combination of product text analysis, network theory and topological based machine learning to study the future performance of companies in financial markets. Our network links are based on the similarity of firms' products and constructed using the Securities Exchange Commission (SEC) filings of US listed firms. We find that several topological features of this network can serve as good precursors of risks or future gain of companies. We then apply machine learning to network attributes vectors for each node to predict successful and failing firms. The resulting accuracies are much better than current state of the art techniques. The framework presented here not only facilitates the prediction of financial markets but also provides insight and demonstrates the power of combining network theory and topology based machine learning.

show abstract

Directionality of real world networks as predicted by path length in directed and undirected graphs

Cited by 11 publications

References 43 publications

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Estimating the impact of structural directionality: How reliable are undirected connectomes?

BFS based distributed algorithm for parallel local directed sub-graph enumeration

Topology of products similarity network for market forecasting

Contact Info

Product

Resources

About