In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself. There are several different types of cycles, principally a closed walk and a simple cycle.
A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. In a directed graph, each edge must be traversed by the walk consistently with its direction: the edge must be oriented from the earlier of two consecutive vertices to the later of the two vertices in the sequence. The choice of starting vertex is not important: traversing the same cyclic sequence of edges from different starting vertices produces the same closed walk.
A simple cycle may be defined either as a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex, or as the set of edges in such a walk. The two definitions are equivalent in directed graphs, where simple cycles are also called directed cycles: the cyclic sequence of vertices and edges in a walk is completely determined by the set of edges that it uses. In undirected graphs the set of edges of a cycle can be traversed by a walk in either of two directions, giving two possible directed cycles for every undirected cycle. A circuit can be a closed walk allowing repetitions of vertices but not edges; however, it can also be a simple cycle, so explicit definition is recommended when it is used.
A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red)
Cycles in undirected graphs:
Cycles in directed graphs:
If you accumulate data on which you base your decision-making as an organization, you should probably think about your data architecture and possible best practices.
If you accumulate data on which you base your decision-making as an organization, you most probably need to think about your data architecture and consider possible best practices. Gaining a competitive edge, remaining customer-centric to the greatest extent possible, and streamlining processes to get on-the-button outcomes can all be traced back to an organization’s capacity to build a future-ready data architecture.
In what follows, we offer a short overview of the overarching capabilities of data architecture. These include user-centricity, elasticity, robustness, and the capacity to ensure the seamless flow of data at all times. Added to these are automation enablement, plus security and data governance considerations. These points from our checklist for what we perceive to be an anticipatory analytics ecosystem.
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Hello! Today I’ll be going over graphs . These data structures are the most widely used on the web, given the countless forms that a graph can organize values or even the data structures that can be made from them. In fact, the worldwide web itself can be represented as a graph. Let’s jump right into it!
A week ago we learned about graph data structure. Today we will talk about how we can work with graphs. We will try to find distances between two nodes in a graph. This is one of the main uses of graphs and it’s called graph traversal. There are two main graph algorithms Breadth First Search (BFS) and Depth First Search (DFS) and today we will talk about BFS.
This is how our graph looks like:
Breadth First Search
In our example we will work with an adjacency matrix. This is how matrix represents graph above:
We will start with an input node, then visit all its neighbors which is one edge away. And then visit all their neighbors. Point is to determine how close the node is to the root node.
Function which we will write in a moment will return an object with key value pairs where key will represent node and value how far this node is from the root.
First we will loop over the adjacency matrix (2D array), create as many key value pairs as many nodes we have on the graph. Initially we will assign distance to the infinity which represents lack of connection between the nodes.
In a previous blog post we talked about how to apply the Breadth First Search algorithm to the graph data structure. Today, let’s figure out how Depth First Search (DFS) works.
DFS is one of the fundamental algorithms used to search nodes and edges in a graph. It’s a form of a traversal algorithm.
Just a reminder, this is how our graph looks:
And this is our adjacency matrix (read here about adjacency matrix representation):
Based on the name we can assume that BFS focuses on the depth of the graph. The search starts at some root node and it keeps searching as far as possible each branch before backtracking.
Our task is to write an algorithm that explores routes as deep as possible before going back and exploring other routes. Let’s see how we can do it.
The opportunities big data offers also come with very real challenges that many organizations are facing today. Often, it’s finding the most cost-effective, scalable way to store and process boundless volumes of data in multiple formats that come from a growing number of sources. Then organizations need the analytical capabilities and flexibility to turn this data into insights that can meet their specific business objectives.
This Refcard dives into how a data lake helps tackle these challenges at both ends — from its enhanced architecture that’s designed for efficient data ingestion, storage, and management to its advanced analytics functionality and performance flexibility. You’ll also explore key benefits and common use cases.
As technology continues to evolve with new data sources, such as IoT sensors and social media churning out large volumes of data, there has never been a better time to discuss the possibilities and challenges of managing such data for varying analytical insights. In this Refcard, we dig deep into how data lakes solve the problem of storing and processing enormous amounts of data. While doing so, we also explore the benefits of data lakes, their use cases, and how they differ from data warehouses (DWHs).
This is a preview of the Getting Started With Data Lakes Refcard. To read the entire Refcard, please download the PDF from the link above.
#big data #data analytics #data analysis #business analytics #data warehouse #data storage #data lake #data lake architecture #data lake governance #data lake management