The diagram is a visual representation of a relationship illustrated with edges (lines or arrows), which is widely used in industrial and scientific communication. Although recognizing diagrams is essential for vision language models (VLMs) to comprehend domain-specific knowledge, recent studies reveal that many VLMs fail to identify edges in images. We hypothesize that these failures stem from an over-reliance on textual and positional biases, preventing VLMs from learning explicit edge features. Based on this idea, we empirically investigate whether the image encoder in VLMs can learn edge representation through training on a diagram dataset in which edges are biased neither by textual nor positional information. To this end, we conduct contrastive learning on an artificially generated diagram--caption dataset to train an image encoder and evaluate its diagram-related features on three tasks: probing, image retrieval, and captioning. Our results show that the finetuned model outperforms pretrained CLIP in all tasks and surpasses zero-shot GPT-4o and LLaVA-Mistral in the captioning task. These findings confirm that eliminating textual and positional biases fosters accurate edge recognition in VLMs, offering a promising path for advancing diagram understanding.