Identifying network structure similarity using spectral graph theory

Gera, Ralucca; Alonso, Lazaro; Crawford, Brian; House, Jeffrey; Méndez-Bermúdez, J. A.; Knuth, Thomas; Miller, Ralph E.

doi:10.1007/s41109-017-0042-3

Cited by 49 publications

(40 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, we focused on scaling and universality from a random matrix theory point of view. We would like to stress that even though we already have some previous experience with scaling studies of random network models (see, e.g., [ 5 , 15 , 16 , 17 , 32 ]), this is the first time we apply this technique to non-Hermitian adjacency matrices.…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, random weights have been used in other complex network models; see some examples in [ 14 , 15 ]. We have named this model as the ER fully -random network model [ 5 , 16 , 17 ]. The sparsity

is defined as the fraction of the

independent non-vanishing off-diagonal adjacency matrix elements.…”

Section: Introductionmentioning

confidence: 99%

“…As precedents, we can mention that we have already studied some spectral [ 16 , 17 ], eigenvector [ 16 ], and transport [ 5 ] properties of ER-type random networks with a special focus on universality, from a random matrix theory (RMT) point of view. Moreover, we have also performed scaling studies on other random networks models, such as multilayer and multiplex networks [ 15 , 31 ] and random-geometric and random-rectangular graphs [ 32 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Martinez-Martinez

Méndez-Bermúdez

2019

Entropy

View full text Add to dashboard Cite

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivity α , and the losses-and-gain strength γ . Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i γ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ ≡ ξ ( N , α , γ ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ < 0.1 ( 10 < ξ ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1 < ξ < 10 . Moreover, to extend the applicability of our findings, we demonstrate that for fixed ξ , the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.

show abstract

Section: Discussionmentioning

confidence: 99%

is defined as the fraction of the

independent non-vanishing off-diagonal adjacency matrix elements.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Martinez-Martinez

Méndez-Bermúdez

2019

Entropy

View full text Add to dashboard Cite

show abstract

“…Then, to identify ER-normal ceRNA network comparable to ER+ normal reference ceRNA network, we applied different correlation cutoff values (0 to 1 with a step size of 0.01) on the miRNA target site share network for ER-normal samples, and select the correlation cutoff values that makes ER-normal ceRNA network most similar to ER+ normal reference ceRNA network. To estimate topological similarity, we employed normalized Laplacian Matrix Eigenvalue Distribution that discovers ensembles of Erdős-Rényi graphs better than other metrics such as Sequential Adjacency or Laplacian [30]. After identifying the ER+ normal reference network and the corresponding ERnormal network, we used the same cutoffs (0.6 for ER+ subtypes and 0.68 for ER-subtypes) to construct the ER+ tumor network and the ER-tumor network, respectively.…”

Section: Building Subtype Cerna Networkmentioning

confidence: 99%

“…Since normal samples should have similar molecular dynamics between ER+ and ER-, we sought to find the co-expression cutoff for ER-normal network that yields the most topological similarity to the ER+ reference network. To estimate topological similarity, we employed a normalized Laplacian Matrix Eigenvalue Distribution that discovers ensembles of Erdős-Rényi graphs better than other metrics, such as Sequential Adjacency or Laplacian [30] (see Methods). While ER-normal network topology changes drastically if different correlation cutoff values are used (S. Fig.…”

Section: Two-step Pairwise Normalization Of Er+ and Er-cerna Networkmentioning

confidence: 99%

3′-UTR shortening contributes to subtype-specific cancer growth by breaking stable ceRNA crosstalk of housekeeping genes

Fan

Kim

Bai

et al. 2019

Preprint

View full text Add to dashboard Cite

ABSTRACTShortening of 3′UTRs (3′US) through alternative polyadenylation (APA) is a post-transcriptional mechanism that regulate expression of hundreds of genes in human cancers. In breast cancer, different subtypes of tumor samples, such as estrogen receptor positive and negative (ER+ and ER-), are characterized by distinct molecular mechanisms, suggesting possible differences in the post-transcriptional regulation between the subtype tumors. In this study, based on the profound tumorigenic role of 3′US interacting with competing-endogenous RNA (ceRNA) network (3′US-ceRNA effect), we hypothesize that the 3′US-ceRNA effect drives subtype-specific tumor growth. However, we found that the subtypes are available in different sample size, biasing the ceRNA network size and disabling the fair comparison of the 3′US-ceRNA effect. Using normalized Laplacian Matrix Eigenvalue Distribution, we addressed this bias and built the tumor ceRNA networks comparable between the subtypes. Based on the comparison, we identified a novel role of housekeeping (HK) genes as stable and strong miRNA sponges (sponge HK genes) that synchronize the ceRNA networks of normal samples (adjacent to ER+ and ER- tumor samples). We further found that distinct 3′US events in the ER- tumor break the stable sponge effect of HK genes in a subtype-specific fashion, especially in association with the aggressive and metastatic phenotypes. Knockdown of NUDT21, a master 3′-UTR regulator in HeLa cells, confirmed the causal role of 3′US-ceRNA effect repressing HK genes for tumor growth. In this study, we identified 3′US-ceRNA effect on the sponge HK genes for subtype-specific growth of ER- tumors.

show abstract

A nonparametric change detection approach in social networks

Hazrati‐Marangaloo

Noorossana

2021

Quality & Reliability Eng

View full text Add to dashboard Cite

A network provides powerful means of representing relationships between entities in complex physical, biological, cyber, and social systems. Any phenomena in those areas may be realized as changes in the structure of the associated networks. Hence, change detection in dynamic networks is an important problem in many areas, such as fraud detection, cyber intrusion detection, and health care monitoring. This article proposes a new methodology for monitoring dynamic networks for quick detection of structural changes in network streams and also estimating the location of the change-point. The proposed methodology utilizes the eigenvalues for the adjacency matrices of network snapshots and employs a nonparametric hypothesis to test if the distribution of the eigenvalues for the current snapshot is different from those of the previous ones along a sliding window of reference networks. The statistic of the nonparametric test, energy distance among eigenvalues, is monitored using a one-sided exponentially weighted moving average control chart. Then, after an anomaly detection signal from the monitoring scheme, eigenvalues for the snapshots are employed to calculate the energy statistic at various time steps to locate the change-point.The proposed method is intended to detect two types of structural changes in the networks: (1) change in the communication rates among individuals and (2) change in the community structure of the network. The proposed methodology is applied to both simulated and real-world data. Results indicate that the proposed methodology provides a reliable tool for monitoring networks streams and also estimating change-points locations for precise assessing of the networks under investigation.

show abstract

Identifying network structure similarity using spectral graph theory

Cited by 49 publications

References 48 publications

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

3′-UTR shortening contributes to subtype-specific cancer growth by breaking stable ceRNA crosstalk of housekeeping genes

A nonparametric change detection approach in social networks

Contact Info

Product

Resources

About