Software-Defined Networking (SDN) has evolved network management by detaching the control plane from the data forwarding plane, resulting in unparalleled flexibility and efficiency in network administration. However, the heterogeneity of traffic in SDN presents issues in achieving Quality of Service (QoS) demands and efficiently managing network resources. SDN traffic flows are often divided into elephant flows (EFs) and mice flows (MFs). EFs, which are distinguished by their huge packet sizes and long durations, account for a small amount of total traffic but require disproportionate network resources, thus causing congestion and delays for smaller MFs. MFs, on the other hand, have a short lifetime and are latency-sensitive, but they account for the vast bulk of traffic in data center networks. The incorrect use of network resources by EFs frequently disturbs the performance of MFs. To meet these issues, precise classification of network traffic has become crucial. This classification enables traffic-aware routing techniques. This paper offers a novel model for classifying SDN traffic into MF and EF using a spike neural network. Once identified, traffic is routed based on the classification results. For MF, the model uses the Dijkstra algorithm. For EF, the Widest Dijkstra algorithm is used. This model solves the difficulties of traffic heterogeneity in SDNs by integrating advanced classification techniques and strategic routing algorithms. It enables desirable resource allocation, eliminates congestion, and increases network performance and dependability. The models used have proven their efficiency by outperforming the traditional Software Defined Network and other algorithms in terms of: throughput by 60%, and 20%, bandwidth utilization by 5%, and 7%, packet loss by 50%, and latency by 60%, respectively.