## 4 Main Tools of the WSN-DPCM Platform
### Tool for WSN Application Planning and RF Simulation
#### 4.1.3 Topology Reduction  
The usefulness and added value of the PT towards network deployment definition is significantly enhanced through a set of novel algorithms developed in the context of the WSN-DPCM project that allow the developer to evaluate network connectivity and propose alternative connectivity scenarios. It is noted that respective algorithms developed are based on RSSI values provided by the RF simulator or real measurements acquired from a network deployment. To the best of the authors' knowledge, it is the first time that well-known graph theory algorithms have been utilized to extract useful information about a network topology as well as to attempt to offer alternative topologies. Figure 6: Graphical representation of the connectivity matrix. Network Connectivity Evaluation  
Based on the connectivity matrix, these algorithms exploit graph theory in a novel approach that allows the developer to identify critical characteristics of the network (assuming a specific topology scenario) which can have a great impact on network performance and robustness. This effectively allows the developer to modify the deployment accordingly until the topology satisfies all requirements. Specifically, through these algorithms the developer is notified if the network is segmented (_i.e._, there is a node or group(s) of nodes that cannot communicate with some other group(s) of nodes) or regarding the existence of a critical node (_i.e._, a node that segments the network if it fails). Also, performance-wise valuable indications are offered regarding the number of hops that separate each node from the nearest (or the assigned) gateway. Furthermore, awareness on possible congested areas can be deduced through the number of neighbors of a specific node. In order to achieve the aforementioned objectives, we use two approaches. One is based on Algebraic Graph Theory (AGT) to represent network topology as a graph and analyze it using linear algebra and matrix theory [38]. The other approach is based on Depth First Search (DFS) [39] to obtain accurate results on connectivity evaluation, on checking for network segmentation and for critical nodes. The developed algorithms are presented and evaluated in [40]. In this paper, the topology evaluation algorithms are tested in various network topology scenarios in MATLAB and manage to identify in all cases: (1) if the network is fully connected or not; (2) if there are critical nodes; (3) for a partitioned network which nodes are in each partition; and (4) if there are isolated nodes. The developed tools have been fully integrated in WSN-DPCM Planning Tool, as shown in Figure 7, in which a 2 km\({}^{2}\) area has been covered using 20 nodes. In this case, the analysis results show that the network is fully connected and has no critical nodes. Moreover, the average number of neighbors is indicated (15 in this case), which, in combination with data traffic patterns, can reveal possible congestion hot spots in the network. Also, all nodes are able to directly communicate with the gateway, since no indication appears under the \"Maximum number of hops to the ROOT\" metric. This case will be utilized in the following as a reference scenario to present approaches able to suggest alternative topologies. Alternative Reduced Topology Indication  
To further enhance PT features, a more experienced developer can set specific parameters or requirements. In this respect, another group of algorithms was designed, implemented and integrated in the context of the WSN-DPCM project that is able to suggest alternative routes or parameters in  
Figure 7: WSN-DPCM Integrated Network Evaluation Algorithms results: graphical (**a**) and statistics (**b**). order to meet specific requirements. All the above form a group of valuable and easy to use tools that are missing in the state of the art environments.