As an industry, the topic cluster is being heralded as one of the greatest templates for setting up a website to rank favourably for target keywords by interlinking in a well-knotted format. Hubspot has put together a great resource on topic clusters and provided an experiment carried out by their former team members that indicates that effectively interlinked pages had better placements on Google’s SERP. A quick note to add is that internal linking is always a great SEO optimisation strategy, regardless of topic clusters or not.

Topic clusters are significant in SEO and help structure contents and pages in line with an overarching theme and is hierarchically structured to or linked to form sub-pages. The drive here is for businesses and marketers to think about the topics they intend to own and not just keywords. To implement this strategy, pillar pages and content clusters are required. The pillar page contains all the key elements or content areas of the topic. While the cluster content is expected to go deeper into an area mentioned or highlighted in the pillar content.  For example, on a seed term ‘mortgage calculator,’ the pillar page could be ‘Ultimate guide to using a mortgage calculator’ and content clusters pages could be on topics such as ‘What is a mortgage calculator and how does it work’ or ‘types of mortgage calculators explained.” There is no doubt that topic clusters well executed have tremendous benefits. 

Rearranging the content of a website to ensure pages do not cannibalise each other but are interlinked to the central pillar page is likely to assist in enhancing the organic rankings and generating traffic for a website. Frameworks and approaches need to be consistently challenged to give room for innovation and breakthroughs. Sometimes a simple face-lift of an exciting approach is not enough to bring about progress but a paradigm shift. A bold but intellectually grounded approach that complements topic clusters but elevates how search marketers should approach the aggregation of keywords not just based on search volume by a Semrush or Ahref-inspired topic but a fundamental understanding of the key concept or seed term. This ushers in the concept of ‘semantic clusters.’ An approach of breaking down and clustering keywords via a model-driven approach through approaches from cognitive science, causal reasoning and decision theory. It is a better way to approach keyword clustering from a user-first and structured approach. 

Clustering in search marketing should not begin and stop with topic clusters. A sure way of gaining more context-rich insights around a seed term to aid forecasting,  trend analysis and demand intelligence is to develop semantic clusters as part of the clustering exercise. To better explain this position, let’s explore “running shoes” clusters from Semrush. A solely driven topic cluster strategy is fuelled by the search volume of related search terms per pillar page. These terms are clustered based on co-occurrence, syntactic semblance and SERP similarity.  

On the other hand, semantic clusters focus more on a meaning-first and model-driven approach. It views keywords as concepts by creating semantic relations or edges based on the seed keyword or term. You can safely say, it is a user-first approach that maps or models the clustering based on how people view and engage with the concept in a real world. I can confidently say it is a cognitive, contextual, causal and decision-framed approach. By clustering search terms using deep cognitive, causal and decision models we cover all aspects of the meaning of the concept and can target relevant keywords even if there is no search volume generated by keyword research and SEO tools. To make the case for semantic clusters stronger, it is important to use an established framework or in this case a scaffold. This is where a tool like ConceptNet comes into place. 

Exploring some of the ConceptNet relations that will serve as a premise for developing Semantic Clusters

ConceptNet is a multi-lingual knowledge graph or a semantic network used to represent commonsense knowledge about the world. 

Below are some of the core semantic relations or edges that is demonstrated for a concept like a ‘car’

IsA: Represents a subclass relationship (e.g., “A car IsA vehicle”).

PartOf: Indicates that something is a part of a larger whole (e.g., “Engine PartOf car”).

HasProperty: Attributes a property to a concept (e.g., “Car HasProperty Loud”).

UsedFor: Describes the typical use of an object (e.g., “Car UsedFor transportation”).

CapableOf: Indicates an ability or function (e.g., “Car CapableOf moving”).

Causes: Represents a causal relationship (e.g., “Car Causes traffic”).

HasA: Specifies a necessary part ot attribute (e.g., “Car HasA windshield”).

MadeOf: Indicates materials used to make a concept. (e.g “Car MadeOf metal”)

Some of these relations can form the foundation for building semantic clusters. This will be developed further in subsequent blogs to clearly establish why more efforts should be taken to transcend beyond topic clusters to semantic clusters. 

Why the search intent is more complex to classify

Analysing and modeling the user search intent goes beyond the simplistic categorisation of informational, navigationals, transactional and commercial. Users are quite complex and the purpose of their search can’t be easily inserted into the four boxes of categorisation that is common in most search platforms, articles and commentaries.

The search intent is usually conceived as the purpose behind a search. Keyword search data on third party software tools, Google Search Console and Google Keyword planner are a goldmine for data-centric marketers. The user intent should focus on the purpose, motivations and reasoning behind a search. There are user stories, prompts and triggers around the public and private  keyword data. Reducing use intent to general actions that suit us as marketers deprives us from gaining deeper insights as to why users are searching in the first instance.  

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A simplified analysis of the 0-1 knapsack problem

In our previous article, we touched on the Travelling Salesman problem and highlighted how it belongs to the subfield of combinatorial optimisation. The topic of combinatorial optimisation seeks to discover the most efficient object from a finite set of items.  The three main combinatorial optimisation problems are Travelling Salesman Problem (TSP), Knapsack problem and Minimum Spanning Tree (MST). Our focus will be on the Knapsack problem in this article. A subsequent piece will touch on MST. 

Diving  into the Knapsack Problem

Let’s now assume a deeper look into the logic of the Knapsack Problem. The decision version of the Knapsack problem is considered NP-Complete. Firstly, we will briefly examine the problem statement. Providing a set of objects with attributable value and weights (Vi, Wi), what is the maximum value that can be attained when the sum of the subsets of these objects are selected to be within the knapsack capacity.

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Exploring the Traveling Salesman Problem (TSP)

Graph theory seeks to address different situations or problems in business application or organisational setups. TSP (Traveling Salesman Problem) is usually considered NP-hard (nondeterministic polynomial time) in solving decision problems. This is because there are more than one possible action or directions when deciding to traverse through every city or vertex in a given graph with the goal or returning to the original. Taking some journey down the historical lane, the TSP problem was formulated in1800s by an Irish mathematician W.R Hamiltion and his British counterpart Thomas Kirkman. 

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Understanding Articulation Points in a graph with examples

Graphs can be directed or undirected in nature. Articulation points are quite important in a graph as they signal possible vulnerabilities in a given network. Removing a node from a connected undirected graph is likely to split the network into different components of an undirected graph. 

A simple illustration of articulation points 

The undirected graph below contains seven nodes and there are two articulation or critical points. Node B is very important to the network as it directly connects with five nodes. Removing node B will break this graph into three disconnected components. The three disconnected graphs after removing node B will be (A) , (C and D) and (E, F and G). The second articulation point on this graph is node C. A decision to remove node C will lead to two disconnected components which are nodes (A, B, E, F, G) and (D). This clearly shows that node B and C are the two articulation points with B being slightly more critical. Node B is the most critical because if removed it renders the remaining graphs into three disconnected components. On the other hand, removing vertex C splits the graph into two disconnected components.

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A practical understanding of topological sorting and ordering 

The shortest path problem is pivotal in graph theory. It aims at discovering the “most efficient’ or ‘best’ way of moving from x to y, where x and y are both nodes in a given graph. The most efficient or best in this context is evaluated by the lowest sum of edge weights between the path of both vertices. The shortest or quickest path is arrived at by summing the lengths of the individual edges. A best-case scenario is a graph with edges having positive weights. There is also the concept of single-source shortest path problem with s as the source node. For clarity, the source node initiates the transversal within the graph.

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Exploring Breadth First Search and Depth First Search in a graph

You might have encountered the words, breadth and depth in real-world scenarios. Breadth implies the complete range of knowledge of any given subject or topic. On the other hand, depth in terms of learning touches on the degree to which a particular subject is magnified or explored. Let’s begin with the breadth first search or the BFS of a given graph. Now BFS does not refer to Best Friends from school but Breadth-First Search. 

Exploring Breadth First Search or Breadth First Traversal 

BFS is an algorithm that is designed to search for a graph or tree data formation. It usually travels in a breadthward motion and utilises a queue as a prompt to identify the next vertex to commence a traversal. If a roadblock is encountered or no adjacent node is found, the tree root or the source node is removed for the queue. The traversal of the graph usually begins with a ‘search key’ or the initialising node. Imagine a hotel with so many floors and rooms as nodes, a breadth-first traversal algorithm is like a cleaning staff that will clean rooms floor by floor. All neighbouring nodes at the current depth or floor with the example above will be visited to clean before moving to the vertices or rooms on the next floor. No node is expected to be revisited as one would not expect hotel staff to clean the same room twice in the same period. Once a room is cleaned, it is ticked on a sheet as a visited while with BFS, the neighbouring reversed node is enqueued or marked as visited, 

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Finding the mother vertex in a graph 

Networks or graphs are pivotal in so many real-world applications such as fraud prevention systems. search engines, recommendation systems, social networks and a lot more. The search for the mother vertex of a graph aids in understanding the accessibility of a given vertex or collection of vertices. 

What is the meaning of the mother vertex in a given graph?

In a given graph G = (V, E), a mother vertex v has a pathway for all other vertices in the specified graph to enable the connection. All other vertices in the graph can be accessed via the mother vertex. A mother vertex is quite common in directed graphs but is also applicable in undirected networks. We will briefly explore mother vertices in different network examples

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The role of the betweenness centrality measure in networks 

Ever wondered how to detect the most influential individual, station, motorway or node in a network? It is not a normal popularity test but a mathematical way for determining a node with the most impact in the flow of information within a network. A very good way of determining nodes that are great connectors for moving from one point of a graph to another. In a real-world situation, when these nodes are removed, the movement to other nodes in the graph becomes quite challenging. With betweenness centrality, the number of paths a node is a part of is also revealed. In a connected graph, the Betweenness Centrality algorithm calculates the shortest path between nodes in the given network. The weight between nodes is quite important in determining the shortest path as factors such as frequency, capacity, time, flow and influence determine these weights. 

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Exploring Dijkstra’s shortest path algorithm

Several graph algorithms can help reveal hidden patterns in connected data. These algorithms can be classified into several categories such as approximations (e.g clustering), assortativity (e,g average neighbour degree), communities (e.g K-Clique) and centrality (e.g shortest path). In this blog, we will be looking at one of the most popular shortest path algorithms known as the Dijkstra’s algorithm. We will look at an example table and code implementation for this algorithm. Shortest path algorithm can be relevant in a traffic network situation a user desires to discover the fastest way to move from a source to a destination. It is an iterative algorithm that provides us with the shortest path from an origin node to all other nodes in the graph. This algorithm can work in weighted and unweighted graph scenarios. 

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