**A Random Graph Model for Power Law Graphs**

We propose a random graph model that could be a special case of sparserandom graphs with given degree sequences that satisfy an influence law. This model involves solely atiny low range of paramo eters, known as logsize and log-log rate. These parameters capture some universal characteristics of huge graphs. From these parameters, numerous properties of the graph will be derived. for instance, for certai n ranges of the parameters, we have a tendency to WI II cypher the expected distribution of the sizes of the connected elements which just about certainly occur with high likelihood. we have a tendency to illustrate the consistency of our model with the behavior of some huge graphs derived from information in telecommunications. we have a tendency to conjointly discuss the brink operate, the enormous part, and also the evolution of random graphs during this model. **[1]**

**A graph model for unsupervised lexical acquisition**

This paper presents associate unattended methodology for aggregation linguistics information from a part-of-speech labeled corpus victimisation graph algorithms. The graph model is constructed by linking pairs of words that participate particularly syntactical relationships. we have a tendency to target the rhombohedral relationship between pairs of nouns that occur along in lists. associate progressive cluster-building algorithmic program victimisation this a part of the graph achieves eighty two accuracy at a lexical acquisition task, evaluated against WordNet categories. The model naturally realises domain associated corpus specific ambiguities as distinct parts within the graph encompassing an ambiguous word. **[2]**

**A Graph Model for Fault-Tolerant Computing Systems**

An approach to fault-tolerant style is delineate during which a system S associate degreed an formula A to be dead by S are each outlined by graphs whose nodes represent computing facilities. A is feasible by S if A is isomorphous to a subgraph of S.A k-fault is that the removal of k nodes (facilities) from S.S may be a k-fault tolerant (k-FT) realization of A if A are often dead by S with any k-fault gift in S. the matter of coming up with best k-FT systems is taken into account wherever A is equated to a 0-FT system. Techniques are delineate for coming up with best k-FT realizations of single-loop systems; these techniques are associated with ends up in Hamiltonian graph theory. the planning of best k-FT realizations of sure kinds of tree systems is additionally examined. the benefits and downsides of the graph model are mentioned.** [3]**

**Voxelwise-based Brain Function Network using Multi-Graph Model**

In the analysis of the functional magnetic resonance imaging primarily based brain useful network, the pairwise correlation between vertices sometimes suggests that the similarity between daring signals. Our analysis found that the low (0:01–0:06 Hz), intermediate (0:06–0:15 Hz), and high (0:15–0:2 Hz) bands of the daring signal don’t seem to be synchronous. Therefore, this paper presents a voxelwise primarily based multi-frequency band brain useful network model, referred to as Multi-graph brain useful network. First, our analysis found the low-frequency data on the daring signal of the brain useful network obscures the opposite data thanks to its high intensity. Then, a low-, intermediate-, and high-band brain useful networks were made by dividing the daring signals. After that, exploitation complicated network analysis, we have a tendency to found that totally different|completely different} frequency bands have different properties; the modulation in low-frequency is over that of the intermediate and high frequency. **[4]**

**Conflict Resolution for Sacramento-San-Joaquin Delta with Stability and Sensitivity Analyses Using the Graph Model**

The goal of this paper is to resolve the strategic long dispute for the Sacramento-San Joaquin Delta California victimization the Graph Model approach for conflict resolution. To facilitate the analysis, a choice web (DSS) has been developed, incorporating multiple-criteria call analysis, stability and equilibrium analysis, and uncertainty analysis victimization the info-gap technique. The DSS has been used on the Sacramento-San Joaquin Delta conflict. when specifying the stakeholders with their preferences and potential selections, the DSS known the foremost strong answer, considering the potential actions and counteractions of all stakeholders. answer hardiness was then tested underneath the uncertainty related to stakeholders’ views, and underneath cooperative and non-cooperative attitudes. **[5]**

**Reference**

**[1]** Aiello, W., Chung, F. and Lu, L., 2001. A random graph model for power law graphs. Experimental Mathematics, 10(1), (Web Link)

**[2]** Widdows, D. and Dorow, B., 2002, August. A graph model for unsupervised lexical acquisition. In Proceedings of the 19th international conference on Computational linguistics-Volume 1 (pp. 1-7). Association for Computational Linguistics. (Web Link)

**[3]** Hayes, J.P., 1976. A graph model for fault-tolerant computing systems. IEEE Transactions on Computers, (9), (Web Link)

**[4]** Voxelwise-based Brain Function Network using Multi-Graph Model

Zhongyang Wang, Junchang Xin, Xinlei Wang, Zhiqiong Wang, Yue Zhao & Wei Qian

Scientific Reports volume 8, Article number: 17754 (2018) (Web Link)

**[5]** Al-Juaidi, A. E. and Hegazy, T. (2017) “Conflict Resolution for Sacramento-San-Joaquin Delta with Stability and Sensitivity Analyses Using the Graph Model”, Journal of Advances in Mathematics and Computer Science, 20(5), (Web Link)